Lecture on Open quantum systems.ipynb

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    "# Quantum noise in photosynthetic light harvesting\n"
   ]
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    "### & a short introduction to open quantum systems\n",
    "\n",
    "\n",
    "\n",
    "Neill Lambert, RIKEN, nwlambert@gmail.com\n",
    "\n",
    "#### Partially based on:\n",
    "\n",
    "- EPFL summer school lecture Jupyter Notebook version: http://goo.gl/LpUaR1  \n",
    "\n",
    "- Ahsan Nazir's Lecture Notes on Open quantum systems \n",
    "\n",
    "- \"The theory of open quantum systems\" by H.-P. Breuer and F. Petruccione.\n",
    "\n",
    "- Robert Johansson's series of Lectures on QuTiP \n",
    "https://github.com/jrjohansson/qutip-lectures\n",
    "\n",
    "- Uses QuTiP\n",
    "http://qutip.org/\n"
   ]
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   "source": [
    "\n",
    "\n",
    "# Outline:\n",
    "\n",
    "## Part 1\n",
    "\n",
    "- Motivation: Examples of electronic coherence in photosynthetic light harvesting\n"
   ]
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    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "\n",
    "- Modelling noise: The Lindblad Master equation; a quick derivation, and how to evaluate using QuTiP\n",
    "\n",
    "- Introduction to QuTip\n",
    "\n",
    "- FMO example\n",
    "    \n"
   ]
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    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion\n",
    "\n",
    "- Comparing different methods\n",
    "- Evaluating efficiency\n",
    "- Conclusions "
   ]
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   "source": [
    "## Part 1: Motivation"
   ]
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   "source": [
    "Every quantum system inevitably interacts with its environment.  \n",
    "\n",
    "In general, it is impossible for us to model the whole dynamics of the system and environment.\n",
    "\n",
    "So the goal of the theory of open quantum systems is to construct minimal solvable models and methods which account for the influence of the environment on the system.\n",
    "\n",
    "<center>\n",
    "\n",
    "<img src=\"sys-env.png\" height=\"400\" width=\"400\"/>\n",
    "</center>"
   ]
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    "\n",
    "# The motivation for the study of open quantum systems arises from:\n",
    "\n",
    "1. **Describing real experiments** involving quantum degrees of freedom in contact with an environment, and real measurements, e.g.,\n",
    "\n",
    "2. Understanding how the classical world arises from the quantum one.\n",
    "\n",
    "3. Often we want to preserve quantum effects (quantum computation). Noise models are important for error correction, etc.\n",
    "\n",
    "\n"
   ]
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   "source": [
    "## Quantum optics\n",
    "\n",
    "Many of the tools we use in open-quantum systems were developed to descibe interactions between atoms and light in cavities, as typified by the experiments of Serge Haroche (Nobel Prize in Physics 2012)\n",
    "\n",
    "A | B\n",
    "- | - \n",
    "![alt](QED.png) | ![alt](brume.png)\n",
    "\n",
    "Brune et al, 1996."
   ]
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   "source": [
    "## Quantum computing & quantum technologies\n",
    "\n",
    "Artificial atoms are now used as the basis of quantum technologies, but are also subject to various noise sources.\n",
    "\n",
    "A | B\n",
    "- | - \n",
    "![alt](nakamura.jpg) | ![alt](ibm.jpg)\n",
    "\n",
    "\n",
    "First observation of coherent oscillations: Nakamura, Pashkin, Tsai (NEC) 1999\n",
    "Basis of modern quantum computing schemes (Photo from IBM)"
   ]
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   "source": [
    "\n",
    "\n",
    "## Photosynthetic light-harvesting\n",
    "10 years ago similar apparent \"coherent oscillations\" were obseved in experiments on the Fenna-Matthews-Olsen complex from green sulphur bacteria (Nature Physics, Engel et al. 2007)\n",
    "\n",
    "A | B\n",
    "- | - \n",
    "<img src=\"fmo.png\" width=\"600\" height=\"600\" />| <img src=\"fmoexperiment.png\" width=\"600\" height=\"600\" />\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Panitchayangkoon et al. PNAS (2010).\n",
    "\n",
    "Does this mean quantum coherence is important for light-harvesting?  "
   ]
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    "In this lecture I will try to:\n",
    "    \n",
    "    1) Explain, with a simple example, how we can (minimally) model the features of ''electronic coherence''.\n",
    "    \n",
    "    2) How noise from the environment can be taken into account with various degrees of accuracy.\n",
    "    \n",
    "    3) Argue that a \"quantum noise\" model is neccessary in this case, and how coherence and noise optimize effiency of light-harvesting.\n",
    "    \n",
    "    4) Simultaneously, show everyone how to use QuTiP (Quantum Toolbox in Python)"
   ]
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   "source": [
    "## A basic model of photosynthetic light-harvesting\n",
    "How do we make a (very) minimal model of a single excitation being transported through the complex?  Lets focus on just two sites  (chromophores)\n",
    "\n",
    "<center>\n",
    "<img src=\"simple2.png\"/>    \n",
    "\n",
    "</center>\n",
    "\n",
    "We write the states as either both chromophores unexcited, or an electronic excitation on either chromophore.\n",
    "\n",
    "We ignore double excitation."
   ]
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   "source": [
    "If we focus on a single excitation subspace (let us ignore the ground-state), we can  just describe the two molecules as an effective spin:\n",
    "\n",
    "<center>\n",
    "<img src=\"simple3.png\"/>    \n",
    "</center>\n",
    "We can write the energy  of these two levels in the form of a Hamiltonian, using the Pauli spin matrix:\n",
    "<br>\n",
    "<br>\n",
    "<center> $H_E = \\frac{\\epsilon}{2}\\sigma_z$, $\\quad$ $\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix}$ </center>\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "<center> $\\sigma_z = |X_1, 0_2 \\rangle \\langle X_1,0_2| -|0_1,X_2\\rangle \\langle 0_1,X_2|$ </center>\n",
    "\n"
   ]
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   "source": [
    "## What about coupling between molecules?\n",
    "\n",
    "There is typically a dipole coupling between nearby chromophores.  This is a dipole energy coupling:\n",
    "<center>    \n",
    "<img src=\"simple4.png\"/>    \n",
    "</center>"
   ]
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   "source": [
    "In the single-excitation subspace, we can again ignore the ground state, and write\n",
    "<center>\n",
    "<img src=\"simple5.png\">\n",
    "</center>\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "<center> $H_{D} = \\frac{\\Delta}{2}\\sigma_x$</center>\n",
    "<br>\n",
    "\n",
    "<center> $\\sigma_x = |X_1, 0_2 \\rangle \\langle 0_1,X_2| + |0_1,X_2\\rangle \\langle X_1,0_2|$, $\\quad$ $\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$<center>\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "Combining the two:\n",
    "<br><br>\n",
    "<center>$$H= H_S + H_D = \\frac{\\epsilon}{2} \\sigma_z + \\frac{\\Delta}{2}\\sigma_x $$</center>"
   ]
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   "source": [
    "Lets imagine we put an excitation on the first chromophore, and allow it to evolve under this simple Hamiltonian, what happens?\n",
    "\n",
    "The initial condition is $$|\\psi(t=0)\\rangle = |X_1,0_2 \\rangle$$\n",
    "\n",
    "The dynamics are given by the standard time-independant Schrodinger equation\n",
    "\n",
    "$$\\frac{d}{dt}|\\psi(t)\\rangle = \\frac{-i}{\\hbar} H|\\psi(t)\\rangle$$\n",
    "\n",
    "Typical parameters for $\\epsilon = -120$ cm$^{-1}$, and $\\Delta = 87$ cm$^{-1}$.\n",
    "\n",
    "Note, to convert 1 cm$^{-1}$ = $100 \\times h \\times c$ Joules, c = speed of light, h = Planck's constant.\n",
    "\n",
    "In units of $s^{-1}$, 100 cm$^{-1}$ corresponds to $10^4 \\times h \\times c/2\\pi \\hbar = 3\\times 10^{12} s^{-1} = 3 THz$, i.e., a frequency with a time-scale of ~$333$ femto-seconds.\n",
    "\n"
   ]
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   "source": [
    "Let us solve this example using QuTiP, and plot \n",
    "<br>\n",
    "<center> $$P_1(t) = |\\langle X_1,0_2 | \\psi(t)\\rangle|^2$$ </center>"
   ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The history saving thread hit an unexpected error (DatabaseError('database disk image is malformed')).History will not be written to the database.\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
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   "source": [
    "%pylab inline\n",
    "from qutip import *"
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   "source": [
    "\n",
    "\n",
    "psi0 = basis(2,0)\n",
    "tlist = linspace(0,0.333e-12,1000)\n",
    "H = (-120 * sigmaz() + 87 * sigmax()) * 3e10 * 2 * pi\n",
    "output = mesolve(H,psi0,tlist,[])\n",
    "energies, states = H.eigenstates()\n",
    "\n",
    "Pana = [abs((psi0*psi0.dag()).matrix_element(psi0,states[0])**2*exp(-1.0j*energies[0]*t)+\n",
    "         (psi0*psi0.dag()).matrix_element(psi0,states[1])**2*exp(-1.0j*energies[1]*t))**2 for t in tlist]\n",
    "\n",
    "\n"
   ]
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   "execution_count": 3,
   "metadata": {
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   "outputs": [
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sHEeiY6ZkzfkXnRl661QAYqsP01JvjDDsDs07lZpfzSjbFbIuhVqGkQ8M7vA5AijoeIGUskBKuVRKOQ54xHKsqv2c5W8msBMYp4Lm7jNVSfzuRw5oLMQ+2LcPQBAyI9ammRJAQaQSN6Xr99s0HEchNU1wlLFUj7b+UOeOBMYOIMttOG24kLYpy6ZhOQqBZxQz95s/TTMNahnGISBWCBEjhHAHlgHfGe0khAgSQrTreRh403I8QAjh0X4NMANIUUl3txi4RMmUIguMTKk77P1KGds/XYWCkpysxI1rkhE33eHVshsYz1FaH3rE5mG9cO02+lPJzoLhNg/L3mmsbGRE7WHMCIbdOkUzHaoYhpSyFbgP2AycBlZLKU8JIZ4UQrSPepoDpAkhzgADgfa9HEcCSUKI4yid4U9LKXVlGEOviacGHyLacihJNrZtvRS3vTmLJCZwxeA0m4c1cMlUUhnBicrBl77YyWlshMOHlfkrU6baZuRaR0bMi8CMC/sNL78kxw818zh/4sPAe/CPVG//i86oNvVDSrkB2NDp2GMd3n8EfNTFfXuBRJsL7AMu7i6k95/EuModZK06QMhouxjgpQkN5Q3E1x7EhTZqr7L9FrdDl46hv3cqdVWwtARC+r6tg8OSvLWYwS21eI8agr+/7Q1jmqVlJWlfC2BMfL0Ye5L9eJqHuesG6P2u933HmOltJTJm/Jg/8yj7ymK1lqJrzryfhButnPVMxC/Cz+bhubrCJMs24QeMLqaLUv+flWQwjH+KX6sS3qhRsMW0gKOZfpSmqDOq0V7Za5muokYz7sUwDMNKuK+4ncf4M+vSbTfqxxGo2KTk2sUx6nXcTZ0KoRSQsV5XLZm6w+uokit5ThmjSniurhDs24gXjWR9YLRLXQhploza+hyz2MW0KdpM2GvHMAwrMcXSD3XoELQZ+yldEPdkZac1MXmSamFe67qBAsKZ9dH9qoVpjwwuUeIm7Hr1OlUr45RBCfXbDcO4EEVJ+fyp5ld8IpYyfITtmwovhmEYVmLgQFgYeow7a1/g7BZjmOCFCC9UMqWQRRNVC3PojeMBiK04aOyOeAFKTxYT1pZPDT5EX6XeqCWvyxXD8E/Zp1qY9kbuJ4cByAqYYLNldLqLYRhW5FG3v/MCD1Dy3latpeiSyqwKolozaMCTIVer13QXMnoQ+S5R+FJL5henVQvXnsj+WMmU0v0nqDqLOPpmpTYzpPIw5lZtm1v0SsNXSiGreoR6hawLYRiGFWkeN1l5c/iwtkJ0ypGT7tzMKv4T9TRu/dQdFZM3SGkCK95gxE1X1O1SMqWqYRNUDXfg2FCKTKH4U03ujgxVw7YXfNKUuPGcoW7cdIVhGFYkYJ4SoUG5xnLaXXHwlDeruZnMa36pethNCUqzVNshI266wvO08n9xn6Z+KTY3SPndnPvciJvOSLMk+rxSyIlYYtQwHIqY68cCMLQ+2VjsrgvaK14TNUj3vrMVwwjINGoYXXGr+IAp7Cfkh1epHnbavHu4nf+xveky1cPWOwX7cwmSZZwXA4iYHqm1HMMwrIlfhB9ZbrF40EzWF8YQzs7M2/IQP+V1Jo1uUj3sqOsVw4ipOU5bi9FW3pHCQsgs9CLVbwpDJg249A1Wxn/ZQt7mdnae7byAtUH67gLyCScrcKLmHd5gGIbVKRykZEwlm4zqdUfOp5Zyd/U/eJ4HGJGg/t6SQSODWRqyh3DOcTbDSPYdaa/5TZgAJg3+NRMsTfNHjoDsvIa1k7OlZhqDyWf9nZ9oLQUwDMPqtCSOp4wBFGXUaS1FV3wzCsdvvM1XqL0QcvoMavAzxiR0wu2lf7KJ+dwSuEmT8MPC4Ha/tTxR+Utyv8679A1ORHtaHTPVS1shFgzDsDJtv3iQYEr5Z4sxSawjNTuVlF8xRLuOu/FK5Y8jRuXvOwQc2858thAfXqVJ+ELAPR7/5Ze8SMFaYwJfO9IsST1YDWjT79cVhmFYmbGT3ADB8ePQauzY+g2ep5ShgW5TtRsaODM0nU9ZwuJ3lmmmQW9IsyS6TImbcA1H4dSNUNJF4z7Dzds5tzeH7Ap/9rtexmCdLLZsGIaVCQyE6GiQDQ2cOd6gtRzdEFGiZASDFmtnGPGTfVjCOiaUbjQmiVkoOlJAiLmYStGfyDlDNNPhdZmSLvzOGO2F7eR/pvwvTP19Edr3dwOGYdiEF10fpAZfyl//3mrtTkllVgURbbnU46XqshOdCRk9iEJTGP5Uk7crUzMdeiL/82MAZPmP1XQUTsS1llFsFYeRZqPnG6Bxr1LIqhs+XmMl32IYhg3wjQ7ClTbaDhilJYDUveXsYhbJfpdp1uHdTl6Q8uM7t86IG4C6vcpe59XR6qxQeyHCpgymTAQRKMvJ35urqRa90C9diRuPKWM1VvIthmHYAJ/ZSvW6f6bRHgtwoGwoc9jFGzdt0VoK9XGKYTTvMwwDwCNVyZRM47Q1DGES5ARazHy98bsBiDivxM2g+drGTUcMw7AB7ZPEhlQfNdrKgeNKumesDgpKXtPHAeCTeVxjJfrgk9ZreJM7GLB4qtZSKB8xjf1MIStP/Xk6eqMio5ywtnzq6Efk5UO1lvMNhmHYgOCEEIpNg/CllnN7c7SWoznn95/FlRbG6KCgFLZQERFZYRhGQwM8W/xDVri8yZDFI7WWQ8k9TzCN/axpvEZrKZqTs05Jn1neiZo343ZEVcMQQiwQQqQJIdKFEL/v4nyUEGKbECJZCLFTCBHR4dxtQoizltdtauruDXkBowE4tzFZYyXa0lLfwurTo6jBl9HD6rWWQ/j0KN51vZ1nzQ9SUujce2OcPAlmM8TFgaen1mpgtPKTIdm5fzIA7G8cy7V8xo6Zf9RayndQzTCEEC7Av4CFQDywXAjReVOE/wNWSilHA08Cf7PcGwg8DkwBJgOPCyEC1NLeG2pjlNTfeMC5S7LZm9PwoJli13D8BvXTWg4mVxP/nvw//sFDJJ/ST8lNC/LXHWEJnzJ7eKHWUgDFuDxc2zBlnKGmTP31xvTEwbMBrOdaXK5ZrLWU76BmDWMykC6lzJRSNgOrgCWdrokHtlne7+hwfj6wVUpZLqWsALYCC1TQ3GvqrruVH7CG9z3v1FqKppRsVQyzMFgH7VEW2pvGnL0kO+CzN/mU6/lB4ztaSwHAzQ0Ous/gDCPIXuvcHd/t/X56aMbtiJqGEQ50XCgm33KsI8eBGyzvrwd8hRADunmvrhh8zVg+5gfsTI+49MUOTMshZZx/4wj9pPwJsdUsYCNiwxdaS9EU/xzFMX1n6CduagYp83Qqdjmvm7c2tPDAsdt5gOdIHKWvOSlqGkZXs4I6/zd+A8wWQhwFZgPngNZu3osQYoUQIkkIkVRaWtpXvX0iLg5cXSE9HeqceB1CX8toJK+p+smUJvc7yUYWsXDvo1pL0QxplkRXK5ny4MWjNVbzLa3xihZ53HkNI3tzGj8yv80Dri/j56+TKd4W1DSMfKDjiigRQEHHC6SUBVLKpVLKccAjlmNV3bnXcu1rUsqJUsqJwcHB1tbfI9zd4YHQD/mPXEHGZyc11aIl7aORwhfpxzCir0kEIKYhhZb6Fo3VaMO5vTn4U0WpCCZk9CCt5XyD72VKOgnIdd6+Pz0247ajpmEcAmKFEDFCCHdgGbCu4wVCiCAhRLumh4E3Le83A1cJIQIsnd1XWY7pmutc1rOC16nctE9rKZpQklxEsCyhCj/CZ0RrLecbfMN8yXEdggfN5Gw9o7UcTSjYqGRKuQFjdLExTzvttZ3ommTMbfpqjlGL5iQlbhqGO7FhSClbgftQMvrTwGop5SkhxJNCiGstl80B0oQQZ4CBwF8t95YDf0YxnUPAk5ZjuqYlXolwecw5q9dH8oJJ4CRPjlqjq0wJoDBYyZiKtzhnSbZ+n/K9a2L0lSkFjxpIiWkgftRw7utsreVogm+G/ppx21F1HoaUcoOUcriUcqiUst0MHpNSrrO8/0hKGWu55qdSyqYO974ppRxmef1PTd29xWe6kin55zqnYRw/6UIKCbRcrv4+0Zei0VJ6aznsnHHTkFOCGYHrRP1lSu1zmAo2OWfcDLY047ZPMtUTxkxvG/JN9boq2SlX4DxxQvk7Wj99qt/gOVkR5ZPhnDWMX5hexpca/O+44dIXq8yehU8xnsN86arrkfM2ofRkMSHmYqrwI+KyaK3lfA/DMGxIyOhBlIkg+lNJwcF8reWozg0bf8or/JyxocVaS/keofMVwzBVVWisRH1qayEjA1rcvBkxTvvJlJ0ZMH8iRxnP0RQPraWozpnDNWxkAUcCr8Tkoq9mXDAMw6YIkyC3v2WJkA3OVZJta25jQfl7/Jz/EJuog3UnOjF49hDC+1UwoWU/ZWVaq1GXUyclUsLIkcpoPr3RXiM97lw/GQCSKoexiI2s+oE+99IxDMPGlAyfyTbmkp7vXKWlvF2ZeNFIgUsE/pH+Wsv5HiZXE5Gj+wPON+O7+d9vUEAofxB/01pKl8TFwT9Mv+ff6VdQV+Jck5hOnVL+JiRoq+NCGIZhYwp/9gRXsI3P6q7UWoqqFG1TUn5BgE5TPt+WZE8mO9cS9OYTpwiliJCBWivpGnd3uM7tc65gGzmbTmstR1XqDqXgQ41hGM5KojJH7JuSg7PQkKR84boonaZ84BrzZ2QTxZhX79Faiqr45Cpx02+ifuOmNGQUAOd3O88PR5olrxybRg1+jBqo7UoVF8IwDBszciR40Ihn6jGa61u1lqMaHmeV2e0uo/WbKYWP8CGKXALOndBaiqqEVyiZ8MC5+o2b5lhFW9tx51kloejwOfyp5rwYQEh8kNZyusQwDBvj7Q2prokktY0j90vnmVUcVKJkSgEzR2ms5MJEzFcypciaU04z7Lkqp5JB5gLq8WLwrBit5VwQz4lKuvHOdh7DOLdF+c3k+SXobqJrO4ZhqEDxAGU3s5IdzpH4W1thY/MV7GQ2UQu038ntQgQlDOS8GEB/qig6fE5rOaqQu1HJlHK8RuLipt+f/6B5ipmHVThPk1TtQeW7Vkfot+an3xTjQDTEKAmg6bBzJP70dHjA/E9uj9qJT6iv1nIuiDAJ8vyUuGkv3Tk6lV8r3/P8IP1mSgCD5wylEQ/C2/Koyq3SWo4quJxW4kbG6zduDMNQAbexSgLwzHCOTKm9g3+UflujvqFqsCKydr9z1P6+ErN4gOcomHOL1lIuiou7C1sCl/E6P+VscoPWclQhsEBJg/7TDcNwaoJmKwlgYJlzZErF208xihOMjmvWWsqlsYxfdElzDjPfXhDHCzxAv6X6X3bjo8VvsYLXOVqon+XXbYU0SyLrUoBv+9b0iGEYKhA1P442TEQ2p9NY5fh7FY9d9yQnGM2i6lVaS7kk/RZdzkM8zdsuP9FaiirofWJYR9o1OsOQ9Lw8SOQEy/w2EDRS2718LoZhGCrgGeBFrttQXGkjZ0ua1nJsTkipUpMaMEv/udKQxSP5Bw+xKm8GZgefv1eRVclPi/7M9R5fEBWltZpLM2pkG8NJg6++0lqKzTmVIsghmuLxC7WWclEMw1CJV6evZDhpHGnSfybaF5prm4lqOoMZoesRUu0MGACDBinb6Obmaq3GtuR+cYI/8xh/cXkCkx388scE5JJGHA8fu0lrKTbHXmp+dpBsHAO3mVM5y3BOpLhoLcWm5G47ixut5LnG0C9IfyuhdsUNEQf4HX8n97OjWkuxKVV7lVypPFTnuZKFsGlR1OLNQHMR58+c11qOTRn63pO8zY+Z5XdMaykXxTAMlWgfMeTo7bElO5UvWDTAPjIlgBtb3ufv/B7zpi1aS7Ep8qQSN60j7CNuTK4mcrzjAcjb5Ng/nBFn1vNj3mFEWI3WUi6KYRgqkRhRwWvcxd3bbtRaik1pPqL8sBuG2EemBCBGK27umubYo9j88pS48Z5sP3FTEabETdVex40bc6uZqHplhFTkQn3HjavWApyFYWO8ieUtXOraqC+rt5vmmp7inqGsLuo2Rt8JvyMBMxLgHRhQ5Nil2MFVSqYbeoX9xE3ryFFwFsRJxzWMc3tzGEw9RaZQBg0N1FrORTFqGCrh7uNOrnssJqRDL9m8wvs94jmF37JFWkvpNpELlGaP6IbTtDW3aehA1XUAACAASURBVKzGNpxPLSVIllKDD+HTIrWW0218pyjm5pfvuGZe+KXy3c7117+Rq2oYQogFQog0IUS6EOL3XZyPFELsEEIcFUIkCyEWWY5HCyEahBDHLK//qKnbWpQ4+JLNTU2QmuFGmime2Cn6Lil1xD+qPwUuEXjRSN7uLK3l2ITM/SWcIZYsn0TdLmzXFeHzld9MePVppIOuD1l/SMkPaiINw/gGIYQL8C9gIRAPLBdCxHe67FFgtZRyHLAMeKXDuQwp5VjL625VRFuZpmFKgmg57piGkZYGbW0wdCh46m9X1otSYCndFW9zzKaPg3UJjOAML9xgX3MaBo4LY6bPUQbLXIr1tzW8VXA9o+QHplGGYXRkMpAupcyUUjYDq4Alna6RgJ/lvT9QoKI+m+M5QUkQ3lmOaRiVb33KbmbyYL9XtZbSY2pjEskminMZjVpLsQnfjPMfbV/DuoVJwNixNOGJo3Zj7G2exBcswu/yCVpLuSRqGkY4kNfhc77lWEeeAH4ohMgHNgD3dzgXY2mq2iWEmNlVAEKIFUKIJCFEUmmp/nasCpmrVK/Dyh0z5ZsPJjGTPcT55Gstpcdk3f13YshmjcsyraXYhMzjynBNvU8M6wpHXiKkrQ2eOH8/V/MF0UvHay3nkqhpGF01nHZulVwOvCWljAAWAe8IIUxAIRBpaar6FfC+EMKv071IKV+TUk6UUk4MDtbfeiyRc4exRcxnTdv11FQ53joU7avxuo+zv1wpIVH5KThipiTNkvf2xVDIIBJDy7SW02Ou8tzNl8xjxJsPaS3F6mRlQUMDhIVB//5aq7k0ag6rzQcGd/gcwfebnH4CLACQUu4TQngCQVLKEqDJcvywECIDGA4k2Vy1FXH1dOW3iZtITobpqTBlitaKrMvA80puGzzH/gwj3tKbdu50NS2N3rh52lfTzcUoSykhWJ6nCj/8Rg3QWk6PiYlsYxzbOZHpeMucZ+7IYQqFDIpLAPS7d0w7atYwDgGxQogYIYQ7Sqf2uk7X5ALzAIQQIwFPoFQIEWzpNEcIMQSIBTJVU25FHLV63VDeQGRLBq24EHXlcK3l9BgfHzjoMZPzrf4Ot5Vu/mYlseX66Hfrz4vxzVa6tY63la776nfZzzQeqHxCayndoseGIYTwbs+8e4KUshW4D9gMnEYZDXVKCPGkEOJay2W/Bu4SQhwHPgBul1JKYBaQbDn+EXC3lLK8pxr0wJgRjYzjCJXbDmstxarkbE7FBTM57rF4+HloLadXSH9/AEq2O1YfU/U+xTAqwu2v5gcQnBBCmQjCn2oKkxxrK133s5YRUqPtI24uaRhCCJMQ4hYhxBdCiBIgFSgUQpwSQjwjhIjtbmBSyg1SyuFSyqFSyr9ajj0mpVxneZ8ipZwhpRxjGT67xXL8YyllguX4eCnl+t59Xe2Z07SZI0xg1uY/aC3FqrTPLSkJto+E3xX1McqghKYjjlX9EymKAcqR9hs3+ZatdAu2OlbcDChWvk/gZfYRN92pYewAhgIPA4OklIOllCHATGA/8LQQ4oc21OhQtG9uH+5gm9sfr4/lJe6jcOI1WkvpNa6WrXQ90h0rbvqfU76Pz1Q72DP3AlQPVuLGkbbSbWtqJboxFfh2tQG9051O7yuklC1CiCgp5TdDeyxNQh8DHwsh3Gym0MGImBlDA56Ems9RlVOJf5QdDI3oBpsqprCeKXyo762iL8qAmQnwKoSUOo5hSLMkskb5PuFX2UcptksSEuCkY22lm7sjgxiayXeJJCJc/x3e0I0ahpSyxfL2k87nhBBTO11jcAlc3F3I9lI2FsrdlKKxGuvRPqnKHsf5txM1Pw4zgsjmszTXOMZWukWFkhvkR/zW62UGjrHfvbG9r5zOa9zFRrP+9yLvLiU7FPMrDLCfH013+jBuEkI8DfgKIUZ26vB+zXbSHJfzg5QEUvG1Y5SW6soamJr1PmNdTxLb7R4t/dEvqB95rkNwo5WcrY4xUupkiontzGPf+HvtcoRUO9HXjeVnvMZLxTc5zFa69UeU5qi6aAcyDOBrIAUIAP4JnBVCHBFCfA443sBoFWgdriQQecIxDCNnYwrvcyurXZbh7q61mr7x/rhnWMQXJFdHay3FKrQP3x5lv90XgLKV7sCBUFvrOFvpvhr4MFFkU7z8Aa2ldJtL9mFIKc8BK4UQGVLKrwGEEIFADMqIKYMe0m9SAmwGr7w0raVYhfLdSntUaUgCdlzBAKDmiuvZeAgmZMANWouxAoEfv8ZjFDI05FZgmNZy+sTlQ3JoLk4ie0si0Svsb65PZ06lCHKJIuYyrZV0n+40SQmAdrOwvC+XUh6WUtZ1vMagewTfdDmxnGGp2+daS7EKrZbVd5uH2U/V+kI42sTKccfe4k88QaK//RfL765/lo/5AXz6qdZS+kxLi7K6M3y7yoA90K1htUKI+4UQ39l1RQjhLoSYK4R4G7jNNvIck6gEHwr6xXKuyIVyu5x++F28s5Xc1WOC/RvG6JgaHuJpFu/8jdZS+ow0SyJrlbhpny1tz7Qv/+3qACOlcremcaBlHK/6/RYfH63VdJ/uGMYCoA34QAhRIIRIEUJkAmdRFgt8Tkr5lg01OhwmE4xUBko5REk2tFz5EgMvt/9MKTbejb/yCLdXPEdjpX0vdV50+Bz+VHNeDCAoPkRrOX3Gf7qSvgIdYCvdkm0nGMcxxnra1+6b3RlW2yilfEVKOQOIQlnrabyUMkpKeZeU8pjNVTogP/d4k31MpeWNlVpL6RM1hbVEtOXQhDuRc+27jRzAs78nuW7DlGVOtth3H1PBFqVvKc/PPteQ6kzUIsUwoupPY26176FSTYeVuKm3oxFS0MO1pKSULVLKQillZfsxIYTjrTmsAkP7n2cqBzAdtasFd79H1vYsmnAnx3MErp5qLn5sO4qDlB9x2S77LsnWHlD0V0fYV6Z0IfyjAyg0heFNPXlfZWstp094WLYCcB1rX8PXerP44OoOrzXAT22gy+HxnmzZ3D7XvjOlpKZEvKnj+QWbtZZiNRqHWrbSPWbfceOSquiX8Y5hGPDtVrpF2+w7bkJKLGtIzbKvuOnN8ubVUsqbLK8bgS+tLcoZCL1CSSgR1fad8E+dgjZcCZ8YqrUUq9G+AZRnpn3HTXrdIFIZgd+MRK2lWI3aqARacaHipP2uWttc20xk81nMCKLnx2ktp0f0xjD+2unzI9YQ4myET4ukBh9CzMWcT7O/XdDa+WavaPsqKF2UoNnKlxl03n4NQ0q4v/opRpJKxC2ztJZjNXLveBxv6njX526tpfSanK1ncKOVPNch9Avqp7WcHtGdeRi3CSHKhBDlQoiVwHdyN3vdl0JrhEmQ460MwM7bZL8Z0/PbEtnDDLvc+vNCRF05nLMM41hLAvW19tm5mpurzIoODlZejkLspP4042HXowtT8314mof4aujtWkvpMd2pYfwRuBKIA3KAp2yqyImoCFNKslX77DP1V+VUEtd6kvEcIXpcgNZyrIaHnwdLRp7lej4l9Yyam1JajzP7ywmi1KFqfvDtJLfTp6Gt1T533ztUGs3DPM2p6x/VWkqP6c6voVpKeVRKWSKl/CMw2dainIXy6VfzHA+Q1DxGaym9on213Wyvkbi4O84e2GD/M77dVr5BKSE8UvU7raVYFT8/+KTfLeQ2hZC77azWcnqFPa/v1R3DCBVCrBBCzBRCBAPG3hdWwmPZUn7Fc6wvn6G1lF7Rvtpu++q7jkRCAvhRRf6+PK2l9Ir22dDucUM0VmJ9wvtVEEIpxdvt080j965iGntJGNGqtZQe0x3DeBwYDfwFSANGCSE2CCH+JoRYblN1Do69l2LbV9ttX33XkbiiYR1V9Gfex/doLaVXBBYqE8P6X2aHxdhLUBelpLfGw/b3w2msbOT/im5lN7OIi23TWk6P6c5M79eklPdJKWdLKQOBIcDLQCWwyNYCHZmICJjufZyFZSspPVt56Rt0hm+ukil5TXa8TGnQDGXW+qBy+8uUzK1mouqVJSciFzqembuMVr6T+1n7i5uczam4YCbXbRie/h5ay+kxPe7Rk1LmSyk3SCn/LqX8UU/uFUIsEEKkCSHShRC/7+J8pBBihxDiqBAiWQixqMO5hy33pQkh5vdUtx4RAv4j7mYlt5G/7ojWcnpMeKXygw27wvEypagrYmnGjcjWLGqL67SW0yPy92TjTT1FplD6xzjOYIR2BlgmuwWV2J9hlO1UClnFwfZZyFJtCIhlp75/AQuBeGC5EKLzwr6PAqullOOAZcArlnvjLZ8TUBZDfKXTzn92S6VlpFTNfvtK/OdLzfzR/Cdedn2A8OlRWsuxOm793MjxUPZcyNlkXwvEFW5VMqX2WdGORuQCJduIakyjtdG++gFaLFsBtK8mYG+oOWZwMpAupcyUUjYDq4Alna6RgJ/lvT9QYHm/BFglpWySUmYB6TjIaK22kZaEk2JfhnHqtInXWcHKcc9hcrXPoaeXojREiZvyr+wrbhqSFL01UfZZir0UPoN8yHONxoNmcrenay2nR3hltm8FYJ9xo+YvPRzoOOQk33KsI08APxRC5AMbgPt7cC+W0VxJQoik0tJSa+m2Kb5TlEzJP9++MqWTSiHWLocGdpf2DaHaku0rblb5rWAu2yhd4rjLvH0+4jfcz4ucKgzUWkqPCD2v/HBC7HQrADUNo6v1lTvPvFkOvCWljEDpUH9HCGHq5r3tHfQTpZQTg+1kemv4VUrCiaw5hTTbz0Qk0+fruIX3mDS4SGspNsNzouKG3tknNVbSM/afHcAO5jrEpkkXInvxvbzM/RzJt599PurKm/BtrVD6xubZ52bGahpGPjC4w+cIvm1yaucnwGoAKeU+wBMI6ua9dsnAcWFU4U+ArKAk2X4y36l7n+U9fsgk9+NaS7EZQUtnsYCN3Ov2utZSuk1bG6SmKu/taevPnmKPQ9JPZ3oQSDlXDs/F3ds+p7OpaRiHgFghRIwQwh2lE3tdp2tyUTZoQggxEsUwSi3XLRNCeAghYoBY4KBqym2IMAlyfBOox4uc3Tlay+kW0iwZbFllt72G5IhETwxih/sCDhWEU12ttZrukbMzi3eabuSx/i/i53fp6+2VUcMa+QFrGPPVS1pL6TaKuQkGjR2ktZReo5phSClbgfuAzcBplNFQp4QQTwohrrVc9mvgLiHEceAD4HapcAql5pECbALulVLa36yXC/DW9evwpYZ9cqrWUrpF6cliBsjzVOHPoAnf60pyGFxdIc6y+nRKirZaukvJ5qPcyEdc7bZJayk2JW64mQ+5md8V/Yrm2mat5XQLR+j3U3V4i2X+xnAp5VAp5V8txx6TUq6zvE+RUs6QUo6RUo6VUm7pcO9fLfeNkFJuVFO3rYmeMAAzLnZTvc7fpKT8bN9RDrH158X4kf863uVWat7rXBnWJ+2zn9tnQzsq/YL6ke8agxut5H55Rms53eK6d5ZylLFc5nFIaym9xjHHQ9oZ37THnrSPTu/2OSNV4Y6dKQFM9DjBrbyP295dWkvpFu2zn13G2HExtpsUDVDSX8kO+yhpRZclMZbjRI/x11pKrzEMQweMiq7lAJP5cH+kXYyUEilKDcOc4PiZktdEJVPyybGPTCm4RImbAXa29WdvqB+ipL/mo/qPm+r8asLb8mjEg8jLh2otp9cYhqEDQmK8GSYyiJD5FB3R/+Cv2vJmGvHAf5rjZ0oD5yrfMbxC/0NrW+pbiGo6gxlB1IKRWsuxOW5jLVvpZujfMHI2KBrtfSsAwzB0gDAJ8nyVxF+wVd+JX0pY3vQ2PtQStsxxtv68EINnD6EBT0LN56jK0fcCkTlfnsWdFvJcY/AO8dZajs1p30o3pEzfvxmAyvatAAbadyHLMAydUBVhWVPqgL4Tf34+VFdDQJArIWGuWsuxOS7uLmR7KaX19g2j9Ep6OqzhB5yIcI5FpKPmx9GEO3XNbjTV63vQpDlZqaG2jLDvZlzDMHSCjFcMw+W0vg3j1NFmQJKQoKy26wy0bxBVsUffcbOvKp6bWMPXy+xnbkJf8OzvyfjYWkZzgrR0fTfz+OQqaaffJKOGYWAF/Cz9Af0L9J0peb72IpX055ct/6e1FNWoGTuLdVxDalWo1lIuij1v/dlbRoxSZkzrfUj6v+S9/I3fM3DRBK2l9AnDMHRC+7o/kbUpuh4p5Zp6En+qCYz00VqKarTecRdLWMfq+qu1lnJRXA/tI4RiEuL1m36sjTIkXZJ6tEFrKRekvBz+V3Edf+n3NwZPCdNaTp8wDEMnBCeE8JzXH3iQ58jP0W977Ddbf86w76p1T7CHdYuaqpt4N3cmBYQRF9OktRzVmCu3UUowi97R727R7ekmPh5Mdp7j2rl8x2LdlL/yP+7kVJo+O5PNrWai65WOX0fc+vNCREdDqFclQ4q+pjxPn7vvZW9KxZU2ct2G4tnfU2s5qhE+LoQgzjPwvH7dvOzTPazgVeYNto8Z6RfDMAwd0V6SPanTIf95u7PoRwNFplAChtrXPgR9wWSCL8UVfM1l5H2mz610S7cnA1AUMkZjJeoSdeVwWnEhsiWDhnJ9NksN2Pw+r3I3C1rWay2lzxiGoSMmDi7mNt7C+/MPtZbSJYWblUwpP2C0xkrUpzxUcfOqvfosybYdVpaZbxrhXHHj4edBjnssJiQ5m1O1ltMl/XOV343vZfZv5oZh6Ijxvmd5izuYc/AfWkvpksYDSqZUO8S5MiWAthGKYUidVv98spRMyWuK88VNabASN+d368/MpVkSXaPETeTV9h83hmHoiOhrlQQV03BKl5vbf+S2nLt4jYarb9Raiur0m5IIgH/OCY2VdM3gCiVTClto/6XYntI4VDGMlqP6M/NzX2fjRw3FpkEEJ9jP7oAXwjAMHeEX4UeuawyeNJG9OU1rOd9jU9YI/stdRFw/SWspqjP4aiUjjqk+rrthz6UppYSYi6nGl4gZUVrLUR2PiYqZe2fqz8zPbVSMPM9BmnENw9AZBcFKxlS8RV9bn9bUQEYGuLl9u6mQMzFwbChlIgh/qsjfm6u1nO9wvCCYYEp4cPR2h9+fpCsGLp3BfbzEE/JxraV8j4YDimHUxhiGYWADGocrhtGSpC/DyFifwt/5HXdFbMTNPrcj7hPCJMjtr8TNuU36KskmJ0MZwXjMmKi1FE2InhbKW973saFsMmVlWqv5LmUFzVTij+sEx2gqNAxDZ3hOURKWT4a+DKP68938jmdYLj7QWopmbF3yMuHks9V9sdZSvkOyUohltGMUYnuMyfTtdz+ur58Nf2j7MwFU4HvXMq2lWAXDMHRG2ILR1ONFea3OivGWXKk13jFKSr0h9PI4CgjneLK+mn1+/On1fMQNTAw9p7UUzbg67AhP8kdq3/tMaynfUFenrCDs6iqIG6XPybg9xTG+hQMRMWsIgT41VNW6UFwCIToZWOHfPpZ8hpMWY4ExFq/UUym2pb6FGVUb8KCZmklvaS1HMy5zP8gs/sKeXT8GlmgtB4CUI424SBdGjnTDw0NrNdZBtRqGEGKBECJNCJEuhPh9F+efE0Ics7zOCCEqO5xr63BunVqatcDkIkgYrSzV3N7UoDXmVjMx7WPJr3HeGsbIOMlb4g7WpidSW1SrtRwAcraewYNmclyH4Bvmq7UczQiYo6TL4IJjGiv5lsbX36EWH/7S9rDWUqyGKoYhhHAB/gUsBOKB5UKI+I7XSCkflFKOlVKOBV4C1nY43dB+Tkp5rRqatWTMGDDRxukD1VpLAeDc3hz8qKHENNAhxpL3FncPwVSPIyRykqx1+uj4LtmqVHcKg5235gcQc20iZgQxjadprm3WWg4A5mPJeNCMX1SA1lKshlo1jMlAupQyU0rZDKzi4vXG5YDT9q5eZ15LNX6Me/M+raUAULBRyZRyA5y3dtFOaZjyP6jYqY92qeYkpebXGOvchuEzyIdct6G400LWhtNaywG+bcb1meE4vxu1DCMcyOvwOd9y7HsIIaKAGGB7h8OeQogkIcR+IcR1FwpECLHCcl1SaWmpNXRrQtjEMLypJ7hAH5lSVo7gCOOojHW+CXud+abTXycdGd6ZSqbkMdlxMqXeUhgyFoDSL7VvlpJmSUyVkkYGL3YcM1fLMLoaVnKh6bLLgI+klB03hYiUUk4EbgGeF0IM7epGKeVrUsqJUsqJwcHBfVOsIXqrXq9pWsIEjlB071+0lqI5fjOVjDkgVx+GEXFe0RF6VaLGSrSnKU6Jm9bD2sdNwYE8/KmiTAQRMnqQ1nKshlqGkQ8M7vA5Aii4wLXL6NQcJaUssPzNBHYC46wvUT94h3iT4zZMN9Xr9sK0s47z70h7p3907QnMrWZNtRQXtPGy+R4+cl1G5OVdlqGcCq8Z4zlFPBmVQVpLIf9zpZaT03+MQ82+V8swDgGxQogYIYQ7iil8b7STEGIEEADs63AsQAjhYXkfBMwAUlRRrSHt+xqUfqltaamquJG2jCw83CUjR2oqRRcEjQymyBSKL7Xk7srSVMuR4y48xSO8NP0DTK7GlKqwny5iFKd4qOoPSI2X+2rYcxiA6lj73sO7M6qkMillK3AfsBk4DayWUp4SQjwphOg46mk5sErK70T3SCBJCHEc2AE8LaV0eMP4pnp9RFvDyHp/H1kMYY/HPKdcEqQrvoxZwV94hJPp2u5sd8Syl9P48ZrK0A0RERAQAOfPQ8GF2i9UYqXrndzKuzRf7xgzvNtRbeKelHIDsKHTscc6fX6ii/v2Ak7XQNtv+ljYBv4ZRzXVUbldyZXqI4ZrqkNPnL75CZ56Ch7Ogas11OH6+adcjh+TEqYC/TRUog+EUIakp+0sIGWHC+E/HKiZls2pURQQxRM3aCbBJhj1WJ0SedNU7uQNft76kqbVa/cTStWaiY5Vte4LEyz/isOHtdVxS9KDbGcek0OytRWiI/7Q8EcKCMftf69ppqGoSKnh+PnBUAfrWjIMQ6cMGhXEptA7OVCbQEaGhjoKlRpG8Hyj3aOdCeMl0/ma0V+/otneGBXp5xncmk09XkTPH6GJBj3Sb4LS0eaVkqSZhsx39/Iy93J35AZMDpbDOtjXcSwmWlarTtIo7dcU1BDdfIZm3BhyzShtROiQyEj4TFzHM3X3cm5vjiYastYqTZUZPmNx9XDRRIMeCbtW+dFElmhnGM0bt3Evr7DQfZtmGmyFYRg6ZtHgEzzLr3B74z+ahJ+59hgmJBleiXj4OcjqaVZAmATZgUq7VN5n2rRLVe9Uan7lMUbNryNR84ZRhR+h5gKKjmjT8+2VoqQJtymOFzeGYeiYCcG5/IrnGJL0oSbhV25TEn5ppNF/0ZnaOKUk27RHm5Ks+0nFMEwTHC9T6gsmVxOZ/ZX0mvuJNmYeUarEzaDFjve7MQxDx0QtVRLc0MrDmkwSW+n1M6awn8Kbfql62HrHc4YSN75ntMmUwoqUcEMWGIbRmapYxczrd6tv5udTSwlvy6MWb6KvjFU9fFtjGIaOCRk9iEKXcPyoIXvrWdXD33/ci4NMYcg1CaqHrXcilyqZUkzFYdU7vqtLGnFpaaQJd2IWx1/6BifD3bJVrfdp9Q0je61Su8j0HYuLu+P1LRmGoXNyg5XEX/S5uom/rg5SU8HVFRKdbhbMpQmdFEGpCCZQlpO/J1vVsI+e9iSSPBaOKcTdx13VsO2BsB/OYzY7WSY/UH1Ies0uS9/SEMdrjgLDMHRPQ7yS8Jr3q9v0kb4qiQ3m+fxp4Ct4ajuhWZcIkyBnwATKGED6jrxL32BFDh1S/sZOCVQ1XHshavwATgTMJrPMj/x8dcM+UR7OHmZgmjZV3YBVwjAMneMzR6lhBKSrW8OoXP8V89nCTO8jqoZrT2y8YzXBlLK5YZaq4R7+uhGAqY6ZJ/UZIb4dkq725Mp/FP2Ymewh+BfL1Q1YJQzD0DnRN0wgiQnsbphEW9ulr7cWbkf2AyCnTlMvUDtj9AxfQKg+T+bZ9bGkMoIZw4rVDdiOuCloO5+yBI+Xn1UtzPx85eXvDyMcdC6lamtJGfSOoPgQJkQmkZsLc1MhQaX+58gCxTDClhrF2AsxybKfVMrBWtpa+uHiZvvyV+GhfMLa8qnCH99p9rvni61JCK9gGutIOtYI/FqVME+uy2QUdURMjsdkcrwObzBqGHbBNEshf9++i19nLYqOFBDRlksVfgxZbKxpfiHCwmCL17Xk1vQnY90pVcLMXn0AgLMDphhLml+E6BsnAxB7/oBqQ9K9/vcKJxjNb5v/qkp4WmCkODtg+jTJUNIp/mSvKuFlr1JqF+mBk41M6RJ4B3vjShtFn6jj5k07lbipiTdqfhcjdPJgzrkMxp8qMr9QZxOygDNK3PjOm6xKeFpg5AZ2wBWBR0gnluVf3qlKeI2WTKk63ui/uBQtE5X/kWm/OmYecEapYfjMm6JKePZMTth0AAo+sn3ctNQ1E1ut9LAPXW4YhoGGxN4wmnq8GNKcxvm0MpuHt7nuMt7mx3hec4XNw7J3gpcomVJ4ru1rGC31LcRWKz3sQ28xDONStExS4sa072ubh5W+NhkvGsl0G0HgMMcd7mwYhh3g1s+NM/5KD2vGe/ttGlZLC7yQdS238zbDf6LucFF7JPYHY6jHi5iWMzY38/RPT9KPBrLdhhEYO8CmYTkCIdfPACA81/Y1jNL1yu/yXKRjNxUahmEnVI5USkv1X9o28ScnQ0MDxMbCACNPuiRqmvmeomFczXrWT33KpuE4CsOWjmaNyzJebPk5pSW2nfLtcsgyDH2SY9f8DMOwE/pdoRhG/xTbGkbWe3u5jk+4YkypTcNxJCrjlH4MW5v59kO+fMHVuC6/0abhOApu/dx4ZeYHPM+D7N0nbBpWwLmTAIRca9QwrIYQYoEQIk0IkS6E+H0X558TQhyzvM4IISo7nLtNCHHW8rpNTd16YMitSqY0vOogLfUtNgsnfM3zGIvZ/QAAE/lJREFUfMJSlnl8YrMwHA15y63cyGpe4n7bhSFh927l/ezZNgvG4ZiulLPYa0Mvz82FxJbDzPY5TOwNo20XkA5QzTCEEC7Av4CFQDywXAjxnaU2pZQPSinHSinHAi8Bay33BgKPA1OAycDjQogAtbTrgaC4ILLcYhFIUjdk2iQMaZYMO7cLgIgfzrFJGI7IqOWJfMSNbDwWSnOzbcLI2ZHJPwtu5h6flYw0psZ0m8smNXEVmwlc+1+bhbF7N5hxwXf2eIdcobYjatYwJgPpUspMKWUzsApYcpHrlwMfWN7PB7ZKKcullBXAVmCBTdXqkNev/Zz+VLI52zbrDmRuSCVYllBsGkTMVY63lr+tCA6G+Hil7+fgQduEkffODm5mNT/y+wxh29YVh2JqYh0bWcgD6ffSUN5gkzB271QmBjpDzU9NwwgHOi7rmW859j2EEFFADLC9J/cKIVYIIZKEEEmlpY7XBp9w/XCa8WD79ktf2xvOvbcTgIzw2QiTkSv1hNvjD/IGd1L993/b5PnC0h7VNMUYudYTAoYGcsZrDB40c/oN27RL/ead0exmJlckFNrk+XpCTcPoKge60NCFZcBHUsr25fa6da+U8jUp5UQp5cTgYMdbZ+fyy5W/+3a30NJo/ZUIXb9WmqNaL5tj9Wc7OpdF53En/yN0zxqbPD86R4mbQTc7QTHWyhTHzwWg+lPrl7SKjxYwvPkUYzhO4lzHy3M6o6Zh5AODO3yOAC60S/syvm2O6um9DktYGLzb/15y6wJJXWndtg9plgy19F+E32JkSj1l+F1zABhZuZfGykarPvvc3hwi2nKowp9h1xu7WfWUftfMA2BAsvUNI+NN5TeTFjQDV0/HX8tVTcM4BMQKIWKEEO4oprCu80VCiBFAANBx6uxm4CohRICls/sqyzGnY3CYGV9qOb/Guok//WA5heaBFJsGMWRRnFWf7QwMGD6ANM8xeNLE6TetO+s7680dAKSFzHT4TlVbEHfXTFpxYWTtIarzq6367NZtimHUTnCOQpZqhiGlbAXuQ8noTwOrpZSnhBBPCiGu7XDpcmCVlN9uriilLAf+jGI6h4AnLcecDrf5SvXa9/AOqz53y+EBjOMYv74u0+i/6CVFI5U2w6pPrRs3pq1K2ajhsiut+lxnwTfMl9M+k3GljbT/fmW150qzJOasEjchN8+12nP1jKrzMKSUG6SUw6WUQ6WUf7Uce0xKua7DNU9IKb83R0NK+aaUcpjl9T81deuJWEvTR3zF11Zt+ti0Sfk772ovqz3T2fBcqBhG4LFtVnum2QxryueyhSsZfJfTDQy0GufHzOUsw0g5XG+1Z2ZvPcvg1mzOiwHE3eqYe3h3xpjpbWcEjQwm1WssXjRy8l+7rPLMpppm8r9MBSTz51vlkU7JyJ/PoRk3Emr2U372vFWeefQoPF97FyuithAzf7hVnumUPPEEwznLM1nWmyWf+7pSykobfKXTNBUahmGHFI1fDEDd6i+s8ryU1/ZwtHEkX/ksIizMKo90Svwi/NgQvoK/8Cg7t1tn057Nlp66+fMx5l/0gemzXPH1hVOnICfHOs98vepmbuMtqpbfbZ0H2gGGYdghA36sGEZMyudIc98XVav6UCkptY40RuD0lcxfvcwT/Im1X1lniKXbW68zgz0suKLVKs9zVtzdFdMNpYC9/03p8/OamuCTvQNZyW2M+YVzdHiDYRh2Sfztk3nY+0XmtW4mNa3vxc6IZKWm4neT0UbeVxYtUv5u2gRtfZwqU3a6lF+dvZvtzGXulLq+i3Nyfh76KQWEM+zV3/T5Wdu3Q309jB6NU9XKDcOwQ1zcXci//n7SieWLPrZKZW5IZVhTChUigMR7ZlpHoBMzYgTMi0jjjvPPkPxucp+edfof63HBzPGgefhH+ltJofOSuGIaZgSJpdupK+mbAZsffoSXuZefzE63kjr7wDAMO+Waa5S/a9f27Tm5z30MwKkh1+LWz62PqgyEgEdDXuUZfkfVi2/16VmeG5TIbViw1ArKDIJHDSTFezKeNJH8TO+ncbU1tzEl+TXu5RUWzLHuJE29YxiGnbJ4MTzi9g/+uy+e/K9734s38P/bu/f4qMo7j+OfX8IlKkJawl1AZVFuyyXQlBawuHhr3aKiVmitoC20sHS7alnrrV0V8daXu6XgaigKUlbA6ksp4ipokMsiEATkEqUBuYRQQQwk1hRy+e0f58SGySRzMk7OnOH83q/XvDiZ88zJN4fk/GaeeeZ51jkFo8W46xMVLfSyJn8PgIu3LqG6Mr43v8uKy+h/ZAXVCL3vGh37AcaTT0be4GwsWhT3MbY/tYYs/YSPmvek57V9E5QsNVjBSFHnnAPf6biZPhRQOGNJXMfYv+VTOpZ/RBmt6H+nfSgsUfre9nWK0rvRqfoQO+bE96nv7Y8soyWn2N56GO36dUhwwvC66D6nmA8oWkZZcVlcxzjxnPMka1/2mNB9yNUKRgpLGzcWgA6r4nu29IflX6UDH/PwVWvJyMxIZLRQkzRhzyBnvH/JM/EV8+aLFwBw/IqbEpbLQOeh3djWejhnU8770+vMTBTTqc9O0Xe78/fWYcoNiY4XeFYwUtjAu79NKefS+/P32Lv8g0Y9VhXmzYMKWjDy5wOaJmCItZvqXOj7vP8CJ0tPNuqxh4uVtUd7UUwn+k0f2xTxQu3EVWM5RXM+yGv8/KVbZrxOln5CYcs+9L45HJ/urs0KRgrLyMxg68XOhenA/bmNeuzGV4o5UniCLl3gcuuNSrjePxzChxn9aadH2Xxf45a7/cNC4Q6eZOo1RbS9OKuJEoZXnxk3c0GzIibtnsaBA417rM6bD0DRqAmh644CKxgpr919zqdM+2+Z36gVxSpvn8ZhOvHE15aQHo5ZDXwlacLhMVN5iTE8v/ZCz4+rqoKnnnK2J9xmf55NIatHG751Y3uqqyG3Ec+zDhyAiR9PJ1cm0euhHzRdwACz38gU1/vmwew6ezBf1U9Zf7e3PtniDQf5+v7FtOAUl/z70CZOGF7Z/z2R8ee8xDNbcti509tj1j/8Nlfue5q+5/+Vq69u2nxhNnkypFPJ/tl/8jyJ56xZsKO6D3k3PUPH7BB9Wq8WKxhngMP/8jCjeZWfvnUjlR5mkNg9dSbNqGJjtxvp8o1uTR8wpFq3hltucbYfeSR2e61WWv/mVzzNZGYNmmuv/JrQ8OHwVuvrWHB8NBsmzY3ZvvToSX6f6wyRvv32pk4XXFYwzgDfmnElu3qM5s970mIOLz+cf4ic/NkAtHnwTh/Shdtdd8GI9P9j/MIrYg5MyH9wOf3L1nFM2pI9c4I/AUNKBFr+5FYAer78aMyBCe9d9xArTwzhJwM3kJPjR8JgsoJxBmjWDO6919mef+f7DY4vL/z+/ZxNOeu7XE/f8UN8Shhe3bvD9Iue53JWcGzCHfVOFlnxeQVtHrsbgO3fvYfW57X2M2Yo5cy4lt0Z/0jnqiLWX/d4ve3+svkQOeueJJstTJmcmFmIU5aqnpG3wYMHa5hUVqo+1n22VpCuq/r/LGqb/EdXqIKeopnuW/lnnxOG18fbDmuJZKqCrp2yMGqbvMumq4IeTO+u5SXlPicMry3/macK+jda6J7XCursr66q1g3tr1YFXd95jP8BkwDI13quq0m/sDfVLWwFQ1W1YOFmrSDduTD9dMFp+woLVYe03atrGKZ5ox5KUsLwWj3+96qgpbTSgkVbT9u38YHlWkmaKmj+YyuTlDC8Vve8VRW0sEUv/bTw2Gn78i59QBW0RDK1eFNRkhL6ywpGiKy6fqYqaBWieSPu1z2vFegrsw5qhw7O//YVoyq1orwi2TFDp7qqWtd2H6cKepw2unrCXP2goFoff1z1N2m/UAXNG3ZvsmOGUumhUt3dsp8q6PT2/6Wvvaa6Y+Nf9Z3ek1RBK0nTd+95NdkxfWMFI0Sqq6q/6N6oub3DCAXVSy9VLS1NdsLwKi8pd7o1QIvp+MV/URqV+sKoXK2qqEp2xNAq3nhQZ7f/D4VqBdWWlKuCnqS5rvnxvGTH81VDBcO3N71F5CoR+VBECkXkl/W0+Z6I7BKRnSLyP7XurxKRre6t8RPAhIikCSNX3Mu2me+wsf0/cyi9K23P+RtznjjOm2/CuecmO2F4ZWRmkLP/RdZOnM/qzuPo2hUuuwyWLktn7MqJpDWzMSjJ0ulr5zF+76+ZPl0YOBA6X5DBGz2msHfRJobPGZ/seIEhTkFp4m8ikg7sBi4HioBNwDhV3VWrTU9gCfBPqloiIu1V9Yi77zNVbdWY7zlkyBDNz89P2M9gjDFhICKbVTXqEEq/ntLkAIWquldVTwGLgGsi2kwEZqtqCUBNsTDGGBMMfhWMLsDBWl8XuffVdhFwkYisE5F3RaT2AtMZIpLv3n9tfd9ERCa57fKPHj2auPTGGGNo5tP3iTatY2RfWDOgJzASOA9YIyL9VPU40E1Vi0XkQuBtEdmuqnvqHFA1F8gFp0sqkT+AMcaEnV+vMIqArrW+Pg+InIy+CHhVVStU9SPgQ5wCgqoWu//uBVYBg5o6sDHGmNP5VTA2AT1F5AIRaQGMBSJHO70CXAogIlk4XVR7ReQrItKy1v3DgF0YY4zxlS9dUqpaKSJTgTeAdOBZVd0pIg/ijPld6u67QkR2AVXANFU9JiLfBJ4RkWqcAvdo7dFVxhhj/OHLsNpksGG1xhjTeEEYVmuMMSbFnbGvMETkKLA/zodnAZ8kMI5fLLd/UjEzWG4/pWJmgO6q2i7ajjO2YHwZIpJf30uyILPc/knFzGC5/ZSKmWOxLiljjDGeWMEwxhjjiRWM6HKTHSBOlts/qZgZLLefUjFzg+w9DGOMMZ7YKwxjjDGeWMEwxhjjSagLRqxVAEWkpYgsdvdvEJHz/U9Zl4fcE0TkaK1VCn+cjJwRmZ4VkSMisqOe/SIiM92f6X0RyfY7Y5RMsTKPFJETtc7zr/zOGI2IdBWRPBEpcFev/HmUNkE8315yB+qci0iGiGwUkW1u5geitAnkdSQu9a3deqbfcOa02gNcCLQAtgF9ItpMAZ52t8cCi1Mk9wRgVrKzRmS6BMgGdtSz/zvA6zhT4Q8FNqRA5pHAsmTnjJKrE5Dtbp+Ls9pl5O9IEM+3l9yBOufu+WvlbjcHNgBDI9oE7joS7y3MrzC8rAJ4DTDf3f4jMEpEoq3t4ScvuQNHVVcDnzbQ5BrgeXW8C2SKSCd/0kXnIXMgqephVX3P3S4DCqi7YFkQz7eX3IHinr/P3C+bu7fIkURBvI7EJcwFw8sqgF+0UdVK4ATQ1pd09fOSG+B6t6vhjyLSNcr+oPH6cwXNN9zuiNdFpG+yw0Ryuz8G4TzzrS3Q57uB3BCwcy4i6SKyFTgCrFDVes91gK4jcQlzwfCyCqCXNn7zkulPwPmq2h9Yyd+f3QRZEM91LO/hzLszAPgdzpougSEirYCXgH9T1dLI3VEeEojzHSN34M65qlap6kCcheFyRKRfRJPAnuvGCnPB8LoKYFcAEWkGtCH5XRQxc6vqMVU96X45BxjsU7Yvw8v/R6CoamlNd4SqLgeau4t8JZ2INMe56C5U1ZejNAnk+Y6VO8jnXJ3lpFcBV0XsCuJ1JC5hLhheVgFcCox3t28A3lb3naskipk7oi96NE5fcNAtBW5xR+8MBU6o6uFkh2qIiHSs6YsWkRycv6djyU3ljIAC5gIFqvpkPc0Cd7695A7aOReRdiKS6W6fBVwGfBDRLIjXkbj4suJeEKm3VQDnAgtEpBDnGcHY5CV2eMz9ryIyGqjEyT0haYFdIvICzgiXLBEpAn6N8wYhqvo0sBxn5E4h8Dlwa3KS/p2HzDcAk0WkEigHxgbkQjAM+CGw3e1bB7gH6AbBPd94yx20c94JmC8i6TjFa4mqLgv6dSReNjWIMcYYT8LcJWWMMaYRrGAYY4zxxAqGMcYYT6xgGGOM8cQKhjHGBESsCS/jON7/ishxEVkWcf9c99PyNbNBtPJyPCsYxiSIiGSKyJQG9p8lIu+4QzDra7NSRL7SNAlNCphH3Q/+fRlP4AxVjnS7qg5wZ4M4AEz1cjArGMYkTibOzKT1uQ14WVWrGmizIMYxzBks2oSXItLDfaWwWUTWiEivRhzvLaAsyv2l7rEFOAuPU5VYwTAmcR4FerjrNDwRZf8PgFfB+TS+iKx22+4QkRFum6XAOJ/ymtSQC/xMVQcDvwCeSsRBReQ54C9AL5x5uWIK7Se9jWkCvwT6uRPRncadxuVCVd3n3vV94A1VfdjtojobQFVL3AV32qpq0qcZMcnlvrfwTeDFWjOit3T3jQEejPKwQ6p6Zaxjq+qt7u/e74CbgOdiPcYKhjH+yAKO1/p6E/CsO9neK6q6tda+I0BnAjAvlUm6NOB4tCch7uSM0SaW9ExVq0RkMTANDwXDuqSM8Uc5kFHzhdtXfQlwCGeeoVtqtc1w25uQc99r+EhEboQvltYd8GWO6R7jH2q2ge9Sd8LEqKxgGJM4ZThLi9ahqiVAuohkAIhId+CIqs7BmZwu271fgI7APj8Cm2BxJ7xcD1wsIkUi8iOc975+JCLbgJ00YoVNEVkDvIizyl+RiFyJsz7HfBHZDmzHmUAxWtdWHdYlZUyCqOoxEVnnjqF/XVWnRTR5ExiOs6jVSGCaiFQAnwE1rzAGA++6K7OZkFHV+gY8xDXUVlVH1LNrWDzHs9lqjfGJiAwC7lDVaOPia9r8FljqDoc0JlCsS8oYn6jqFiCvoQ/uATusWJigslcYxhhjPLFXGMYYYzyxgmGMMcYTKxjGGGM8sYJhjDHGEysYxhhjPPl/0zJkWxdVqZEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(tlist,expect(psi0*psi0.dag(),output.states), 'b', lw=2)\n",
    "ax.plot(tlist,Pana, 'r--', lw=2)\n",
    "ax.set_xlabel('t (s)')\n",
    "ax.set_ylabel('$P_1(t)$')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<center>\n",
    "<img src=\"fmoexperiment.png\" height=\"600\" width=\"600\"/>\n",
    "</center>\n",
    "\n",
    "**Some questions**\n",
    "\n",
    "1) How can we include noise in a 'quantum model'?\n",
    "\n",
    "2) Are these \"coherent oscillations\" really electronic coherence, and do they play any role in maximizing efficiency of energy transport?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "\n",
    "- Modelling noise: The Lindblad Master equation; a quick derivation\n",
    "\n",
    "- Introduction to QuTip\n",
    "\n",
    "- FMO example\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Part 2: The Lindblad Master equation; a quick derivation\n",
    "\n",
    "One approach we can take to include noise is to treat the environment as a quantum system, but include its affect on the system perturbatively.  This is traditionally done with the Lindblad Master equation.  Let's sketch out its derivation first...\n",
    "\n",
    "Steps:\n",
    "\n",
    "1) A few definitions: density matrix, system and environment (bath) Hamiltonians.\n",
    "\n",
    "2) Born - Markov approximations.\n",
    "\n",
    "3) More definitions: The bath correlation function.\n",
    "\n",
    "4) An explicit example:  the spin-boson model.\n",
    "\n",
    "5) The secular approximation.\n",
    "\n",
    "6) And finally, the Lindblad Master Equation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Definitions: The density operator\n",
    "\n",
    "When a quantum system is effectively \"closed\" we describe its dynamics and evolution in terms of a pure state $|\\psi(t)\\rangle$ whose evolution is determined by a Hamiltonian and the Schrodinger equation (lets make life easier by neglecting $\\hbar$)\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} |\\psi(t)\\rangle = -i H(t) |\\psi(t)\\rangle$$\n",
    "\n",
    "More generally, for open systems it is convenient to use the density operator, which for a pure state, is given by\n",
    "\n",
    "$$\\rho = |\\psi(t)\\rangle \\langle \\psi(t)|$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "When describing one part of a larger composite system, as is the case for open systems \n",
    "<span style=\"color:red\">when we trace out the environment degress of freedom</span>,  the loss of knowledge about the influence of the other systems introduces \n",
    "<span style=\"color:red\">statistical uncertainty</span>. \n",
    "\n",
    "This then gives rise to mixed states, in terms of a statistical ensemble of possible pure states, such that;\n",
    "\n",
    "$$\\rho = \\sum_n p_n |\\psi_n(t)\\rangle \\langle \\psi_n(t)|$$\n",
    "\n",
    "\n",
    "The evolution of the density operator obeys the Liouville-von Neumann equation of motion,\n",
    "\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho(t) = -i [H(t), \\rho(t)]$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "The density operator itself has some important properties;\n",
    "\n",
    "-- For pure states $\\rho^2=\\rho$\n",
    "\n",
    "-- It is Hermitian $\\rho^{\\dagger} = \\rho$.\n",
    "\n",
    "-- It has trace one $\\mathrm{Tr}\\rho = 1$.\n",
    "\n",
    "-- Expectation values of system operators can be evaluated as $\\langle A \\rangle =\\mathrm{Tr}(A\\rho)$.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The system and environment Hamiltonians\n",
    "\n",
    "Ultimately the influence of a large environment on a systems evolution is to induce statistical uncertainty into its dynamical evolution.  \n",
    "\n",
    "This gives rise to dissipation (emission and absorbtion of energy) and dephasing (localization into particular states).\n",
    "\n",
    "The philosophy we will describe here is to start with an \n",
    "<span style=\"color:red\"> explicit Hamiltonian description of the system (**S**) and the full Environment (**E**) </span>, with the Hilbert space\n",
    "\n",
    "$$\\mathcal{H} = \\mathcal{H}_S \\otimes \\mathcal{H}_E$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "and then \n",
    "<span style=\"color:red\"> derive effective models, or equations of motion,</span> for the redused density operator of the system alone, after tracing out the environment degrees of freedom, i.e.,\n",
    "\n",
    "$$\\rho_S(t) = \\mathrm{Tr}_E[\\rho(t)]$$ \n",
    "\n",
    "since $\\rho_S(t)$ descrives all pertinent and accessible information about the system itself.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The full dynamics of the system and environment would in principle be described by the Hamiltonian\n",
    "\n",
    "$$H = H_S + H_E + H_I$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "In general, one can describe the evolution of the whole system and environment, \n",
    "<span style=\"color:red\"> in the interaction picture </span>, as \n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}(t) = -i [\\tilde{H}_I(t), \\tilde{\\rho}(t)]$$\n",
    "\n",
    "where the interaction pictures moves the free evolution of both the system and environment into the operators themselves,\n",
    "such that\n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Formally we can solve the equation of motion with\n",
    "\n",
    "$$\\tilde{\\rho}(t) = \\rho(0) - i \\int_0^t ds [\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$\n",
    "\n",
    "Substituting this into the RHS of the original equation of motion, and formally \n",
    "<span style=\"color:red\"> tracing out the environment degrees of freedom </span>, gives,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) = -i \\mathrm{Tr}_E[\\tilde{H}_I(t), \\tilde{\\rho}(0)]  -  \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Born Approximation\n",
    "\n",
    "This is still an intractable equation of motion.  To make progress we must make a series of \n",
    "<span style=\"color:red\">assumptions</span>:\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "-- \n",
    "<span style=\"color:red\"> **Factorizable initial conditions** </span>: We assume that at $t=0$ the system and environment are seperable, such that \n",
    "\n",
    "$$\\rho(0) = \\rho_S(0) \\otimes \\rho_E(0)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "-- <span style=\"color:red\"> **The Born approximation**</span>: In addition, we assume that the density matrix <span style=\"color:red\">factorises</span> at all times, and that the <span style=\"color:red\"> environment state is time-independent</span>,\n",
    "\n",
    "$$\\rho(t) = \\rho_S(t) \\rho_E(0)$$\n",
    "\n",
    "This assumes that the environment is mostly unaffacted by the interaction with the system. (Any excitations emitted by the system quickly decay in the environment)\n",
    "\n",
    "-- Note: We also remove the first term on the RHS (for many examples it is zero, or it can be cancelled with a c-number term in the system Hamiltonian).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Under these assumptions,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho_S}(s)\\rho_E]$$\n",
    "\n",
    "This equation of motion assumes weak coupling, as the system and environment remain seperable; \n",
    "\n",
    "... but it still includes some <span style=\"color:red\"> time non-local behavior</span> as the state of the system depends on its history (via the integral over $s$), and thus its past interaction with the bath.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Markov Approximation\n",
    "\n",
    "We can now make what is known as the <span style=\"color:red\"> **Markov** </span> assumption, to eliminate this history. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "We assume \n",
    "\n",
    "$$\\tilde{\\rho}_S(s) \\rightarrow \\tilde{\\rho}_S(t)$$\n",
    "\n",
    "in the integral.  \n",
    "\n",
    "This assumptions implies there is a seperation of time scales between environment (**$\\tau_E$**) and system relaxation time (**$\\tau_R$**) and any intrinsic system time scales (**$\\tau_S$**), \n",
    "\n",
    "$$\\tau_E \\ll \\tau_R, \\tau_S$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "I.e., if the environment were to be perturbed by the system, it relaxes back to equilibrium faster than the typical time scale of the evolution (**relaxation** and coherent evolution) of the system. This seems like a consistent assumption to make alongside the **Born approximation**, since that also implies the environment remains in equilibrium.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we have, after substituting $\\tilde{\\rho}_S(s) \\rightarrow \\tilde{\\rho}_S(t)$\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}_S(t)\\rho_E]$$\n",
    "\n",
    "\n",
    "\n",
    "This is sometimes called the Redfield equation; it local in time, but <span style=\"color:red\">not quite completely Markovian</span> (we still have $t$ in the integral limits).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "We can simplifiy this further by removing the reference to $t$ in the limits of the integral, by choosing $s=t-\\tau$, and letting the upper limit go to infinity;  \n",
    "\n",
    "In other words, we assume that the integrand  dissappears fast compared to the system time scales.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "Thus we arrive at the <span style=\"color:red\">fully Markovian master equation</span>;\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  -  \\int_0^{\\infty} d\\tau \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(t-\\tau),\\tilde{\\rho}_S(t)\\rho_E]$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Describing the bath with a correlation function\n",
    "\n",
    "The system depends on the environment properties via the two-time bath correlation functions. For example, lets explicitly define the system-environment interaction term as,\n",
    "\n",
    "$$H_I = A \\otimes B$$\n",
    "\n",
    "where $A$ is a Hermitian system operator, and $B$ a Hermitian bath operator.  (An explicit example will soon make this a little clearer).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "In the interaction picture \n",
    "\n",
    "$$\\tilde{H} = A(t) \\otimes B(t)$$\n",
    "\n",
    "Our Markovian master equation contains terms like:  $\\mathrm{Tr_E}[B(t)B(t-\\tau)\\rho_E]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If we assume the initial state of the environment is a steady state, i.e., it does not evolve under $H_E$, these terms are <span style=\"color:red\">\"stationary\"</span>,  $C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Inserting these various terms into our Markovian master equation, and moving back to the Schrodinger picture, one obtains\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\int_0^{\\infty} d\\tau \\left( [A,[A(-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)A(-\\tau),A]C(-\\tau)\\right)$$\n",
    "\n",
    "This equation in itself is useful, and can be developed and applied to certain problems. \n",
    "\n",
    "However, it is still not in the famous <span style=\"color:red\">**Lindblad**</span> form, and does not guarantee positivity of the density matrix as it is evolved.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note: In general there may be a sum of interactions in the interaction Hamiltonian, in which case the integral contains a sum of terms for each interaction part, and the correlation functions are generalized $\\tilde{H} = \\sum_{\\alpha}A_{\\alpha}(t) \\otimes B_{\\alpha}(t)$\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\sum_{\\alpha,\\beta}\\int_0^{\\infty} d\\tau \\left( [A_{\\alpha},[A_{\\beta}(-\\tau)\\rho_S(t)]C_{\\alpha\\beta}(\\tau) + [\\rho_S(t)A_{\\beta}(-\\tau),A_{\\alpha}]C_{\\beta\\alpha}(-\\tau)\\right)$$\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "Interestingly, there is still not yet any assumption about the timescales $\\tau_S$, due to $H_S$, and the relaxation $\\tau_R$, induced by the bath. \n",
    "\n",
    "If we perform an additional approximation, and <span style=\"color:red\">neglect terms due to system evolution which are very fast compared to the relaxation time scale $\\tau_R$</span>, we can obtain a **Secular master equation** which is in **Lindblad form**. \n",
    "\n",
    "In other words, we will assume, $\\tau_S\\ll \\tau_R$, so that now, the Born-Markov-Secular master equation will be valid when\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "It is a little cumbersome to the general derivation of this step, so let us move onto an explicit example. However, one note;  the above **non-secular** form of the master equation is **may be** applicable even if the relaxation time scale and the system time scale are comparable, and thus it is useful in and of itself. (See Chapter 3.6 in Breuer and Pettrucione).\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The spin-boson model\n",
    "\n",
    "The archetypical example of an open quantum system is where the \"system\" is a two-level system, a spin, described by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<span style=\"color:red\">Pauli spin matrices</span>\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "While the bath is a continuum of <span style=\"color:red\"> boson modes </span>, or harmonic oscillators, described by creation and annihilation operators $b_k$, obeying the commutation relations $[b_k,b_k']=\\delta_{k,k'}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Returning to our example from earlier, our 'spin' was the position of the electronic excitation, and the bosons are the nuclear motion of the chromophores that modulate the energy of the electronic excitations\n",
    "\n",
    "A | B\n",
    "- | - \n",
    " <img src=\"fmo.png\" alt=\"Drawing\" style=\"width: 450px;\"/> | <img src=\"simple2.png\" alt=\"Drawing\" style=\"width: 450px;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The total Hamiltonian is then,\n",
    "\n",
    "$$H= H_S + H_E + H_I$$\n",
    "\n",
    "where\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ H_S = \\frac{\\epsilon}{2} \\sigma_z + \\frac{\\Delta}{2}\\sigma_x$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "$$ H_E = \\sum_k \\omega_k b_k^{\\dagger}b_k$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ H_I = \\sigma_z \\sum_k g_k (b_k^{\\dagger}+b_k)= \\sum_{j,l}c_{j,l} |\\psi_j\\rangle \\langle \\psi_l|\\sum_k g_k (b_k^{\\dagger}+b_k)$$\n",
    "\n",
    "For eigenstates $|\\psi_j\\rangle$ of $H_S$, and $c_{j,l} = \\langle \\psi_j | \\sigma_z  |\\psi_l\\rangle$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the <span style=\"color:red\">interaction picture</span> the interaction Hamiltonian is \n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n",
    "   \n",
    "\n",
    "$$ \\tilde{H}_I =  \\sum_{j,l}c_{j,l} |\\psi_j\\rangle \\langle \\psi_l|e^{i\\Delta_{j,l}t}\\sum_k g_k (b_k^{\\dagger}e^{i\\omega_k t}+b_ke^{-i\\omega_k t})$$\n",
    "\n",
    "$$\\Delta_{j,l} = E_j - E_l$$ is the difference in eigenenergies.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Inserting this into our master equation, we find, \n",
    "\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_z(t),[\\sigma_z(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_z(t-\\tau),\\sigma_z(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "Recall that the bath correlation functions are defined as\n",
    "\n",
    "$$C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$$\n",
    "\n",
    "Where\n",
    "\n",
    "$$B(t) = \\sum_k g_k\\{ b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}$$\n",
    "\n",
    "$$C(t)=\\mathrm{Tr_E}[ (\\sum_k g_k  \\{b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}) (\\sum_{k'} g_{k'}\\{ b_{k'}^{\\dagger}+ b_{k'}\\}) \\rho_E]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Assuming that the initial state of the environment is a thermal state\n",
    "\n",
    "$$\\rho_E = e^{-H_E / k_B T} / Z$$  \n",
    "\n",
    "$$Z=\\mathrm{Tr}(e^{-H_E / k_B T})$$\n",
    "\n",
    "lets us evaluate this quite easily;\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "The only non-zero terms come from \n",
    "\n",
    "$$\\mathrm{Tr_E}[b_k b_{k'}^{\\dagger}\\rho_E]=\\delta_{kk'}[1+n(\\omega_k)]$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathrm{Tr_E}[ b_{k'}^{\\dagger} b_k\\rho_E]=\\delta_{kk'}n(\\omega_k)$$\n",
    "\n",
    "where $n(\\omega) =(e^{\\omega/k_B T} - 1)^{-1}$.\n",
    "\n",
    "Is the Bose-Einstein occupation number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Then\n",
    "\n",
    "$$C(t)= \\sum_k \\left(g_k^2 e^{i\\omega_k t}n(\\omega_k)+ g_k^2 e^{-i\\omega_k t}[1+n(\\omega_k)]\\right)$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can then move to a continuum representation by turning the sum into an integral, and defining the **spectral density**\n",
    "\n",
    "<span style=\"color:red\">\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "**Note: sometimes it is useful to rewrite this in terms of real and imaginary parts. See part 3!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The secular approximaton\n",
    "\n",
    "Let us return to the master equation, in the interaction picture;\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_z(t),[\\sigma_z(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_z(t-\\tau),\\sigma_z(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are going to do two things:\n",
    "\n",
    "    \n",
    "    \n",
    "- Neglect terms come from products of system operators that rotate quickly... this is the <span style=\"color:red\">secular approximation!</span>\n",
    "\n",
    "Its equivalent in this case to a <span style=\"color:red\">rotating wave approximation</span>;  and for it be valid, the relaxation rate has to be smaller than the system frequency.  \n",
    "\n",
    "    \n",
    "- Evaluate the integral over $\\tau$ and $\\omega$\n",
    "\n",
    "This is a lot of algebra, so lets just do one term.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## First, the secular approximation:\n",
    "\n",
    "Recall that, in the interaction picture:\n",
    "\n",
    "$$\\sigma_z(t) =\\sum_{j,l}c_{j,l} |\\psi_j\\rangle \\langle \\psi_l|e^{i\\Delta_{j,l}t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "So the first term in the master equation contains products like\n",
    "\n",
    "$$ \\sigma_z(t)\\sigma_z(t-\\tau)= \\sum_{j,l}c_{j,l} |\\psi_j\\rangle \\langle \\psi_l|e^{i\\Delta_{j,l}t} \\sum_{n,m}c_{n,m} |\\psi_n\\rangle \\langle \\psi_m|e^{i\\Delta_{n,m}(t-\\tau)}$$\n",
    "\n",
    "\n",
    "\n",
    "We neglect terms oscillating very quickly, like <span style=\"color:red\">$2i\\Delta_{j,l}$. </span> (Note we also ignore diagonal terms ($j=l$ etc) just for simplicity, though these can induce additional dephasing contributions).\n",
    "\n",
    "\n",
    "This is similar to a rotating wave approximation, and is valid if $\\tau_S \\ll \\tau_R$  i.e., when the relaxation rate is smaller than the system frequencies.  Now we have the seperation of time scales\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Second, some integrals\n",
    "\n",
    "For the remaining terms, that do not rotate at this frequency, we have to evaluate integrals like,\n",
    "\n",
    "$$ |\\psi_l\\rangle\\langle\\psi_l| \\rho_S(t)  \\int_0^{\\infty} d\\tau e^{i\\Delta_{j,l} \\tau}C(\\tau)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Using our earlier definition of the correlation function\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "We have to evaluate\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i \\Delta_{j,l} \\tau}C(\\tau) =  \\int_0^{\\infty}d\\omega \\int_0^{\\infty} d\\tau e^{i\\Delta_{j,l} \\tau} \\{J(\\omega) e^{i\\omega \\tau}n(\\omega)+ J(\\omega) e^{-i\\omega \\tau}[1+n(\\omega)]\\}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can do the $\\tau$ integral first, using the formula,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{\\pm i\\epsilon \\tau} = \\pi \\delta(\\epsilon) \\pm i \\frac{\\mathcal{P}}{\\epsilon}$$\n",
    "\n",
    "$\\mathcal{P}$ is the Cauchy principal value. The imaginary term leads to environment-induced energy shifts (sometimes called Lamb shifts.  Here we neglect this term, for simplicity.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We see that the delta function lets us then evaluate the frequency integral, and thus,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i\\Delta_{j,l} \\tau}C(\\tau)= \\pi J(\\Delta_{j,l}) (n(\\Delta_{j,l})+1)$$\n",
    "\n",
    "\n",
    "Thus for this term, the right hand side of the master equation becomes \n",
    "\n",
    "$$  |\\psi_l\\rangle\\langle\\psi_l|  \\rho_S(t)  \\left[\\int_0^{\\infty} d\\tau e^{i\\Delta_{j,l} \\tau}c(\\tau)\\right] =  \\pi J(\\Delta_{j,l}) (n(\\Delta_{j,l})+1) |\\psi_l\\rangle\\langle\\psi_l|  \\rho_S(t) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "# The **Lindblad master equation**\n",
    "\n",
    "\n",
    "We are almost there! If we repeat this for each term in the master equation, and collect terms, and move back to the schrodinger picture, we find an equation of motion describing the density matrix of the system alone, which is known as the Lindblad master equation (Gorini–Kossakowski–Sudarshan–Lindblad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\sum_{j>l,l}\\pi J(\\Delta_{j,l})|c_{j,l}|^2 \\left(n(\\Delta_{j,l})+1\\right)\\left[2 |\\psi_l\\rangle\\langle\\psi_j| \\rho_S(t) |\\psi_j\\rangle\\langle\\psi_l|  -  \\{|\\psi_j\\rangle\\langle\\psi_j| ,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\sum_{j>l,l}\\pi J(\\Delta_{j,l})|c_{j,l}|^2 n(\\Delta_{j,l})\\left[2 |\\psi_j\\rangle\\langle\\psi_l| \\rho_S(t) |\\psi_l\\rangle\\langle\\psi_j|  -  \\{|\\psi_l\\rangle\\langle\\psi_l| ,\\rho_S\\}\\right] $$\n",
    "</span>\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "The first part is the \n",
    "<span style=\"color:blue\">coherent system evolution</span>, the second part describes <span style=\"color:green\">spontaneous and stimulated emission</span>, and the third part describes <span style=\"color:red\">absorption</span>.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why is this so great?\n",
    "\n",
    "- This Lindblad form guarantees positivity:  we will always have a physical density matrix.\n",
    "\n",
    "- It is easy to evaluate, and can be derived for many types of systems.  \n",
    "\n",
    "(see part 2 for more examples).\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "# To recap, it is valid when:\n",
    "\n",
    "- The <span style=\"color:red\">**Born approximation**</span> applies:  the coupling is weak such that we can assume $\\rho(t) = \\rho_S(t)\\otimes\\rho_E$\n",
    "\n",
    "- The <span style=\"color:red\">**Markov approximation**</span> applies:  the bath returns to equilibrium on a time scale $\\tau_E$ which is faster than the relaxation of the system induced by that bath $\\tau_R$. \n",
    "\n",
    "- The <span style=\"color:red\">**secular approximation**</span> applies:  the system time scales are small (i.e., higher frequency) than the relaxation time scales.  In other words, $\\epsilon > \\pi J(\\epsilon) (n(\\epsilon)+1)$.\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "** Two questions **:\n",
    "\n",
    "- Can we use this model to describe the environment affecting energy transport in FMO?\n",
    "\n",
    "- Does noise slow down transport, or speed it up?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Solution to the Lindblad master equation\n",
    "\n",
    "In some cases we can get analytical solutions.\n",
    "\n",
    "This is easily done by writing out equations of motion for the matrix elements of the master equation, and assuming the bath spectrum is flat, so that $\\pi J(\\Delta_{j,l})|c_{j,l}|^2 = \\gamma$.  \n",
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\sum_{j>l,l}\\gamma \\left(n+1\\right)\\left[2 |\\psi_l\\rangle\\langle\\psi_j| \\rho_S(t) |\\psi_j\\rangle\\langle\\psi_l|  -  \\{|\\psi_j\\rangle\\langle\\psi_j| ,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\sum_{j>l,l}\\gamma n \\left[2 |\\psi_j\\rangle\\langle\\psi_l| \\rho_S(t) |\\psi_l\\rangle\\langle\\psi_j|  -  \\{|\\psi_l\\rangle\\langle\\psi_l| ,\\rho_S\\}\\right] $$\n",
    "</span>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "which give, for $e=$ excited state, $g=$ ground state, \n",
    "\n",
    "\n",
    "$$\\dot{\\rho}_{ee}(t) = -2 \\gamma (n+1) \\rho_{ee}(t) + 2\\gamma n \\rho_{gg}(t)$$\n",
    "$$\\dot{\\rho}_{gg}(t) = -2 \\gamma (n) \\rho_{gg}(t) + 2\\gamma (n+1) \\rho_{ee}(t)$$\n",
    "$$\\dot{\\rho}_{eg}(t) = - [\\gamma (2n+1) + i\\Delta_{e,g}] \\rho_{eg}(t)$$\n",
    "$$\\dot{\\rho}_{ge}(t) = - [\\gamma (2n+1) - i\\Delta_{e,g}] \\rho_{ge}(t)$$\n",
    "\n",
    "We an see that the populations are coupled with rates corresponding to the emission and absorption.  The off-diagonal matrix elements decay proportional to the coupling the environment.   This is decoherence!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The solutions to these equations are very simple for zero temperature ($n=0$), where we see:\n",
    "\n",
    "$$\\rho_{ee}(t) = e^{-2 \\gamma t} \\rho_{ee}(0) $$\n",
    "$$\\rho_{gg}(t) = 1-2 e^{-2 \\gamma t} \\rho_{ee}(0)$$\n",
    "$$\\rho_{eg}(t) = e^{- \\gamma t}e^{ - i\\Delta_{e,g} t} \\rho_{eg}(0)$$\n",
    "$$\\rho_{ge}(t) = e^{- \\gamma t}e^{  i\\Delta_{e,g} t} \\rho_{ge}(0)$$\n",
    "\n",
    "The off diagonal terms decay at half the speed of the relaxation terms, leading to the infamous <span style=\"color:red\">$T_2 = 2T_1$</span> relationship.\n",
    "\n",
    "In the general case, it can be tedious to construct and solve such equations of motion.  \n",
    "\n",
    "So... lets use QuTiP to play with some examples, and see what noise does to our previous example of pure evolution.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# QuTiP:  A brief introduction\n",
    "\n",
    "The Quantum Toolbox in Python was developed in our group, primarily by Robert Johansson (now working Rakuten) and Paul Nation (now working in IBM-Q).  Continued development by Alex Pitchford, Erik Guigere, Me, and others.\n",
    "\n",
    "http://qutip.org/devs.html\n",
    "\n",
    "It has a variety of built-in solvers for solving the dynamics via: \n",
    "- the Schrodinger equation, \n",
    "- master equations, \n",
    "- Floquet formalism, \n",
    "- Monte-Carlo quantum trajectories, \n",
    "- stochastic Schrodinger/master equations, \n",
    "- the Hierarchy method, the reaction coordinate method, etc.\n",
    "- supports time-dependance in Hamiltonians, Lindblads, etc.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "It based around a quantum object class which can be used to represent state vectors, operators, and superoperators.\n",
    "\n",
    "It is composed of a numerical matrix, and various properties that define its dimensionality, etc.\n",
    "<center>\n",
    "<img src=\"qobj.png\" />\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other reasons to use QuTiP\n",
    "\n",
    "- Open source science\n",
    "- Promotes reproducibility\n",
    "- Has even more functionality, including \n",
    "    - Quantum optimal control library (CRAB, GOAT, and other animals)\n",
    "    - QIP library\n",
    "    - functions to calculate spectra, counting statistics, etc\n",
    "    - Supports arbitrary time-dependance, in Hamiltonian and Lindblad collapse operators\n",
    "    - Active development community."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The history saving thread hit an unexpected error (DatabaseError('database disk image is malformed')).History will not be written to the database.\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recalling our example of a single two-level system described by the Pauli spin matrices\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "In QuTiP we can define this manually, or with predefined operators:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = sigmaz() # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can define and solve the Lindblad Master equation we solved analytically earlier in few lines:\n",
    "\n",
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\sum_{j>l,l}\\gamma \\left(n+1\\right)\\left[2 |\\psi_l\\rangle\\langle\\psi_j| \\rho_S(t) |\\psi_j\\rangle\\langle\\psi_l|  -  \\{|\\psi_j\\rangle\\langle\\psi_j| ,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\sum_{j>l,l}\\gamma n \\left[2 |\\psi_j\\rangle\\langle\\psi_l| \\rho_S(t) |\\psi_l\\rangle\\langle\\psi_j|  -  \\{|\\psi_l\\rangle\\langle\\psi_l| ,\\rho_S\\}\\right] $$\n",
    "</span>\n",
    "\n",
    "QuTiP has several options on how to solve this type of formula.  \n",
    "\n",
    "The default is \"mesolve\" which takes Qobj definitions of the Hamiltonian, and the Lindblad, and converts them into a set of coupled equations in matrix form, as we did earlier. It then directly solves this set of coupled ODEs.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First define the Hamiltonian $H_S = \\frac{\\epsilon}{2}\\sigma_z +\\frac{\\Delta}{2} \\sigma_x$ \n",
    "\n",
    "and initial condition $\\psi(t=0) = |1\\rangle$,  $\\rho(0) = |1\\rangle\\langle 1|$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
      "Qobj data =\n",
      "[[1.]\n",
      " [0.]]\n",
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[1. 0.]\n",
      " [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "eps = -120\n",
    "Delta = 87\n",
    "\n",
    "# Hamiltonian\n",
    "H = (eps * sigmaz() + Delta * sigmax()) * 3e10 * 2 * pi\n",
    "\n",
    "\n",
    "# initial state.  \n",
    "N = 2 # number of states in the Hilbert space\n",
    "n = 0 # the state that will be occupied (python counts from zero)\n",
    "\n",
    "psi0 = basis(N, n)     \n",
    "print(psi0)\n",
    "\n",
    "print(psi0*psi0.dag())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-2.79387047e+13,  2.79387047e+13]),\n",
       " array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       " Qobj data =\n",
       " [[-0.9512125 ]\n",
       "  [ 0.30853651]],\n",
       "        Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       " Qobj data =\n",
       " [[0.30853651]\n",
       "  [0.9512125 ]]], dtype=object))"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.eigenstates()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "We can define our Lindblad master equation by just defining the rates and the operator which goes into master equation.\n",
    "\n",
    "Here we have two operators; one which causes emission, \n",
    "\n",
    "<span style=\"color:green\">$$ \\sum_{j>l,l}\\gamma \\left(n+1\\right)\\left[2 |\\psi_l\\rangle\\langle\\psi_j| \\rho_S(t) |\\psi_j\\rangle\\langle\\psi_l|  -  \\{|\\psi_j\\rangle\\langle\\psi_j| ,\\rho_S\\}\\right] $$\n",
    "    \n",
    "the other absorption\n",
    "    \n",
    "<span style=\"color:red\">$$\\sum_{j>l,l}\\gamma n \\left[2 |\\psi_j\\rangle\\langle\\psi_l| \\rho_S(t) |\\psi_l\\rangle\\langle\\psi_j|  -  \\{|\\psi_l\\rangle\\langle\\psi_l| ,\\rho_S\\}\\right] $$\n",
    "</span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "gamma = 40 * 3e10 #this should be smaller than our system energies.\n",
    "n_th = 0.0 #Start with zero temperure for simplicity\n",
    "\n",
    "all_energy, all_state = H.eigenstates()\n",
    "Nmax = 2\n",
    "sz = sigmaz()\n",
    "collapse_list = []\n",
    "for j in range(Nmax):\n",
    "\n",
    "    for k in range(j+1,Nmax):\n",
    "        #FYI: QuTiPs definition of a Lindblad differs from our derivation by a factor of '2'\n",
    "        rate = np.absolute(sz.matrix_element(all_state[j].dag(),all_state[k]))**2 * 2 * gamma * (n_th+1)\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))  #emission\n",
    "        \n",
    "        \n",
    "        rate = np.absolute(sz.matrix_element(all_state[k].dag(),all_state[j]))**2 * 2 *gamma * (n_th)\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[k]*all_state[j].dag())) #absorption\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Next define the time steps we want to solve the equations for, and run the \"mesolve\" function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# list of times for which the solver should store the state vector\n",
    "tlist = linspace(0,0.333e-12,1000)\n",
    "output = mesolve(H, psi0, tlist, collapse_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Lets also run an example where we start in an eigenstate of the Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "ee = all_state[1]\n",
    "output2 = mesolve(H, ee, tlist, collapse_list)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Calculate some expectation values, and compare to analytical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Since our initial state was the excited state, we can get the probability of being in the excited state\n",
    "#at time t with:\n",
    "Pe = expect(output.states, psi0*psi0.dag())\n",
    "Pe2 = expect(output2.states, ee*ee.dag())\n",
    "\n",
    "#For the case where we start in eigenstate, we can compare this to our analytical result\n",
    "PeAna = [np.exp(-2 * sz.matrix_element(all_state[0],all_state[1])**2 * gamma * t) for t in tlist]\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1,1, figsize=(8,4))\n",
    "axes.plot(tlist, Pe)\n",
    "axes.plot(tlist, Pe2, color = 'g')\n",
    "axes.plot(tlist, PeAna, color='r',ls='--')\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"$\\rho_{11}$\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume non-zero temperature, the steady state (the long-time solution) of the master equation predicts a thermal state.\n",
    "\n",
    "Analytically, setting the LHS of our equations to zero, and solving, gives the disribution:\n",
    "\n",
    "$$\\rho_{ee} = \\frac{n}{(1+2n)}$$\n",
    "$$\\rho_{gg} = \\frac{1+n}{(1+2n)}$$\n",
    "\n",
    "Which is equivalent to the thermal distribution:\n",
    "\n",
    "$$ \\rho = e^{H_S/k_B T}/Z $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets check this two ways in QuTiP.  First with steadystate() function, then with the thermal_dm() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#non zero temperature\n",
    "n_th = 1.3\n",
    "\n",
    "\n",
    "collapse_list = []\n",
    "for j in range(Nmax):\n",
    "\n",
    "    for k in range(j+1,Nmax):\n",
    "\n",
    "        rate = np.absolute(sz.matrix_element(all_state[j].dag(),all_state[k]))**2 * 2 * gamma * (n_th+1)\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))  #emission\n",
    "        \n",
    "        \n",
    "        rate = np.absolute(sz.matrix_element(all_state[k].dag(),all_state[j]))**2 * 2 *gamma * (n_th)\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[k]*all_state[j].dag())) #absorption\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.36111111111111127\n",
      "0.6388888888888888\n"
     ]
    }
   ],
   "source": [
    "            \n",
    "#Set non-zero temperature and get new collapse_list first\n",
    "n_th = 1.3\n",
    "\n",
    "rhoss = steadystate(H,collapse_list)\n",
    "print(expect(rhoss,all_state[1]*all_state[1].dag()))\n",
    "print(expect(rhoss,all_state[0]*all_state[0].dag()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3611111111111111\n",
      "0.6388888888888888\n"
     ]
    }
   ],
   "source": [
    "#Compare to analytical prediction\n",
    "print(n_th / (1+ 2 * n_th))\n",
    "print((1+n_th) / (1+ 2 * n_th))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[0.63888889 0.        ]\n",
      " [0.         0.36111111]]\n"
     ]
    }
   ],
   "source": [
    "#Built in function to calculate thermal state with occupation n_th\n",
    "print(thermal_dm(2, n_th))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Returning back to our example, can be include more chromophores?  \n",
    "\n",
    "In the single-excitation limit, we wrote 2-sites as a 2-level system.\n",
    "\n",
    "For 7-sites we can write a 7-level system with Hamiltonian\n",
    "\n",
    "$$ H = \\sum_{j=1}^7 \\epsilon_j |j\\rangle\\langle j| + \\sum_{j,j'} J_{j,j'} \\left(|j\\rangle \\langle j'| + c.c \\right)$$\n",
    "\n",
    "<center>\n",
    "<img src=\"fmo.png\" height=\"600\" width=\"600\"/>\n",
    " </center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[7], [7]], shape = (7, 7), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[200.  -87.7   5.5  -5.9   6.7 -13.7  -9.9]\n",
      " [-87.7 320.   30.8   8.2   0.7  11.8   4.3]\n",
      " [  5.5  30.8   0.  -53.5  -2.2  -9.6   6. ]\n",
      " [ -5.9   8.2 -53.5 110.  -70.7 -17.  -63.3]\n",
      " [  6.7   0.7  -2.2 -70.7 270.   81.1  -1.3]\n",
      " [-13.7  11.8  -9.6 -17.   81.1 420.   39.7]\n",
      " [ -9.9   4.3   6.  -63.3  -1.3  39.7 230. ]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "H =  Qobj([[200, -87.7, 5.5, -5.9, 6.7, -13.7, -9.9],\n",
    "                    [-87.7, 320, 30.8, 8.2, 0.7, 11.8, 4.3],\n",
    "                    [5.5, 30.8, 0, -53.5, -2.2, -9.6, 6.0],\n",
    "                    [-5.9, 8.2, -53.5, 110, -70.7, -17.0, -63.3],\n",
    "                    [6.7, 0.7, -2.2, -70.7, 270, 81.1, -1.3],\n",
    "                    [-13.7,11.8, -9.6, -17.0 ,81.1, 420, 39.7],\n",
    "                    [-9.9, 4.3, 6.0, -63.3, -1.3, 39.7, 230]])\n",
    "\n",
    "print(H)\n",
    "\n",
    "#Rescale H\n",
    "H =  3e10 * 2 * pi * H\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[7], [1]], shape = (7, 1), type = ket\n",
      "Qobj data =\n",
      "[[1.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "# initial state.  \n",
    "N = 7 # number of states in the Hilbert space\n",
    "n = 0 # the state that will be occupied (python counts from zero)\n",
    "\n",
    "psi0 = basis(N, n)     \n",
    "print(psi0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The interaction with the bath becomes a little more complicated.  Now each chromophore is assumed to interact with an independent bath.  Each bath modules the energy of that chromophore via coupling to the operator:\n",
    "\n",
    "$$H_I = \\sum_{m=1}^7 |m\\rangle \\langle m| \\sum_k g_{k,m} (b_{k,m} + b_{k,m}^{\\dagger})$$\n",
    "\n",
    "But, the derivation is done just as before, and we find we can easily adapt our ealier model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recall that in the Master equation emission and absorption depend on the environment temperature, and the environment spectral density:\n",
    "<span style=\"color:red\">\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "</span>\n",
    "\n",
    "In many cases we just pretend this is not energy dependent.  However, for FMO, it is know that this function has some structure.  In Ishizaki and Fleming PNAS 2012 they argue that the environment has a decay time of between $50$ fs and $200$ fs. We can capture this with a Drude-Lorentz spectral density:\n",
    "\n",
    "$$J(\\omega) = \\frac{2\\lambda \\gamma \\omega}{\\pi (\\omega^2 + \\gamma^2)}$$\n",
    "\n",
    "$\\lambda$ tells us how strong the overall interaction with the environment is\n",
    "\n",
    "$\\gamma$ tell us the bath cut-off, or decay rate, so is inverse of the bath memory time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    lam = 35 * 3e10 * 2 * pi  #35 cm^-1\n",
    "    gamma = (1/(50e-15))   #1/50 fs\n",
    "    return 2 * lam * gamma * (energy)/( pi * ((energy**2) + (gamma**2)))\n",
    "wlist = linspace(0, 200*3e10*2*pi,100)\n",
    "    \n",
    "fig, axes = plt.subplots(1,1, figsize=(6,4))\n",
    "\n",
    "axes.plot(wlist/(3e10*2*pi), [J0(w)/(3e10*2*pi) for w in wlist])\n",
    "axes.set_xlabel(r'$\\omega$ (cm$^{-1}$)', fontsize=20)\n",
    "axes.set_ylabel(r\"$J(\\omega)$ (cm$^{-1}$)\", fontsize=16);   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "#To be more accurate let us use 300 Kelvin as the temperature\n",
    "Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "#Temperature = 77 * 0.6949 * 3e10 * 2 * pi\n",
    "\n",
    "def n_th(energy):\n",
    "   \n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    lam = 35 * 3e10 * 2 * pi\n",
    "    gamma = (1/(50e-15))\n",
    "    return 2 * lam * gamma * (energy)/( pi * ((energy**2) + (gamma**2)))\n",
    "\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    lam = 35 * 3e10 * 2 * pi\n",
    "    gamma = (1/(50e-15))\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n",
    "all_energy, all_state = H.eigenstates()\n",
    "\n",
    "Nmax = 7\n",
    "\n",
    "\n",
    "Q_list = [basis(Nmax, n)*basis(Nmax, n).dag() for n in range(Nmax)]\n",
    "\n",
    "dephasing = 0\n",
    "\n",
    "collapse_list = []\n",
    "\n",
    "for Q in Q_list:\n",
    "    for j in range(Nmax):\n",
    "\n",
    "        for k in range(j+1,Nmax):\n",
    "            Deltajk = abs(all_energy[k] - all_energy[j])\n",
    "            if abs(Deltajk) > 0 :\n",
    "                rate = np.absolute(Q.matrix_element(all_state[j].dag(),all_state[k]))**2 * 2 * pi * J0(Deltajk) * (n_th(Deltajk)+1)\n",
    "                if rate > 0.0:\n",
    "                    collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))  #emission\n",
    "\n",
    "\n",
    "                rate = np.absolute(Q.matrix_element(all_state[k].dag(),all_state[j]))**2 * 2 * pi * J0(Deltajk) * (n_th(Deltajk))\n",
    "                if rate > 0.0:\n",
    "                    collapse_list.append((np.sqrt(rate)*all_state[k]*all_state[j].dag())) #absorption\n",
    "    if dephasing == 1:\n",
    "        for j in range(Nmax):\n",
    "\n",
    "            rate = np.absolute(Q.matrix_element(all_state[j].dag(),all_state[j]))**2 *  pi * J02(0.) * Temperature\n",
    "            if rate > 0.0:\n",
    "                collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[j].dag()))  #emission\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f536315e2e8>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To be more accurate let us use 300 Kelvin as the temperature\n",
    "Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "lam = 35 * 3e10 * 2 * pi  #35 cm^-1\n",
    "gamma = (1/(50e-15))   #1/50 fs\n",
    "tlist = linspace(0,1.4e-12,1000)\n",
    "outputFMO = mesolve(H, psi0, tlist, collapse_list)\n",
    "fig, axes = plt.subplots(1,1, figsize=(12,8))\n",
    "for m,Q in enumerate(Q_list):\n",
    "    axes.plot(tlist, expect(outputFMO.states,Q),label=m+1)\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"Population\", fontsize=16);\n",
    "\n",
    "axes.set_title('Lindblad solution ',fontsize=24)\n",
    "axes.legend(loc=0, fontsize=18)\n",
    "#fig.savefig(\"fmosec2.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f53631569e8>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To be more accurate let us use 300 Kelvin as the temperature\n",
    "Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "lam = 35 * 3e10 * 2 * pi  #35 cm^-1\n",
    "gamma = (1/(50e-15))   #1/50 fs\n",
    "tlist = linspace(0,1.4e-12,1000)\n",
    "outputFMO = mesolve(H, psi0, tlist, collapse_list)\n",
    "fig, axes = plt.subplots(1,1, figsize=(12,8))\n",
    "for m,Q in enumerate(Q_list):\n",
    "    axes.plot(tlist, expect(outputFMO.states,Q),label=m+1)\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"Population\", fontsize=16);\n",
    "\n",
    "axes.set_title('Lindblad solution ',fontsize=24)\n",
    "axes.legend(loc=0, fontsize=18)\n",
    "#fig.savefig(\"fmosec2.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Using the same parameters as above, $\\lambda = 35$ cm$^{-1}$, $1/\\gamma = 50$ fs, $T=300$K, we find...\n",
    "<center>\n",
    "<img src =\"fmosec2.png\">\n",
    "</center>\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Calculates  generic non-secular master equation\n",
    "#This is experimental, and should be used with a grain of salt\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    lam = 35 * 3e10 * 2 * pi\n",
    "    gamma = (1/(50e-15))\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    lam = 35 * 3e10 * 2 * pi\n",
    "    gamma = (1/(50e-15))\n",
    "    return 2 * lam * gamma * (energy)/( pi * ((energy**2) + (gamma**2)))\n",
    "\n",
    "\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "from numpy import matrix\n",
    "from numpy import linalg\n",
    "from qutip import spre, spost, sprepost, thermal_dm, mesolve, Odeoptions\n",
    "from qutip import tensor, identity, destroy, sigmax, sigmaz, basis, qeye, dims\n",
    "from qutip.ui.progressbar import BaseProgressBar, TextProgressBar\n",
    "def Lnonsec(Hsys, Q_list, tlist, initial_state, Temperature,\n",
    "            return_vals, eigen_sparse=False, options=None,progress_bar=None):\n",
    "    \n",
    "\n",
    "    if progress_bar is None:\n",
    "        progress_bar = BaseProgressBar()\n",
    "    elif progress_bar is True:\n",
    "        progress_bar = TextProgressBar()\n",
    "        \n",
    "    if options is None:\n",
    "        options = Options()\n",
    "    output = None\n",
    "    \n",
    "   \n",
    "    \n",
    "    \n",
    "    \n",
    "    dimensions = dims(Q_list[0])\n",
    "    Nmax = dimensions[1][0]        #hilbert space \n",
    "    #Nmax = 2       #hilbert space \n",
    "    \n",
    "    H = Hsys\n",
    "    L=0\n",
    "    PsipreEta=0\n",
    "    PsipreX=0\n",
    "\n",
    "    all_energy, all_state = H.eigenstates(sparse=eigen_sparse)\n",
    "    for Q in Q_list:\n",
    "        Apre = spre(Q)\n",
    "        Apost = spost(Q)\n",
    "        for j in range(Nmax):\n",
    "            for k in range(Nmax):\n",
    "                A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "                #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "                delE = (all_energy[j] - all_energy[k])\n",
    "                if np.absolute(A) > 0.0:\n",
    "                    if abs(delE) > 0.0:\n",
    "                        #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                        X = (0.5  * np.pi * J0(all_energy[j] - all_energy[k])\n",
    "                             * (np.cosh((all_energy[j] - all_energy[k]) /\n",
    "                                (2 * Temperature))\n",
    "                             / (np.sinh((all_energy[j] - all_energy[k]) /\n",
    "                                (2 * Temperature)))) * A)\n",
    "                        #eta = (0.5 * np.pi * gamma *\n",
    "                        eta = (0.5 *  np.pi *\n",
    "                               J0(all_energy[j] - all_energy[k]) * A)\n",
    "                        PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                        PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                                 * all_state[k].dag())\n",
    "                    else:\n",
    "                        #X =0.5  * np.pi* J0(0.) * A * 2 * Temperature\n",
    "                        X = 0.5  * np.pi* J02(0.)* A  * 2 * Temperature\n",
    "                        \n",
    "                        #X =0.5 * np.pi * gamma * A * 2 * Temperature\n",
    "                        PsipreX=PsipreX+X*all_state[j]*all_state[k].dag()\n",
    "\n",
    "        A = Q\n",
    "        L += ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "             +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "             +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "             +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "\n",
    "    #Setup the operators and the Hamiltonian and the master equation \n",
    "    #and solve for time steps in tlist\n",
    "    psi0 = ( initial_state)\n",
    "    output = mesolve(H, psi0, tlist, [L], return_vals, options=options,progress_bar=progress_bar)\n",
    "    \n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For completeness, lets also look at the solution when we include the dephasing terms we ignored (as well as some non-secular contributions)...\n",
    "\n",
    "<center>\n",
    "<img src =\"fmononsec2.png\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5352374400>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resultMEnonsec = Lnonsec(H, Q_list, tlist, psi0, Temperature, [])\n",
    "fig, axes = plt.subplots(1,1, figsize=(12,8))\n",
    "for m,Q in enumerate(Q_list):\n",
    "    axes.plot(tlist, expect(resultMEnonsec.states,Q),label=m+1)\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"Population\", fontsize=16);\n",
    "\n",
    "axes.set_title('Non-secular solution',fontsize=24)\n",
    "axes.legend(loc=0, fontsize=18)\n",
    "#fig.savefig(\"fmononsec2.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIiIiQUqIdgChkJ2d7fr16xftMERERESkg/vkk0+2OedyGm7vEEl1v379WLBgQbTDEBEREZEOzszWNbZd5R8iIiIiIkFSUi0iIiIiEiQl1SIiIiIiQVJSLSIiIiISJCXVIiIiIiJBUlItIiIiIhIkJdUiIiIiIkHqEH2qRURERGR/lZWVlJSUsGvXLmpra6MdTpsUHx9Peno6Xbt2JTk5udXXUVItIiIi0gFVVlayfv16srKy6NevH4mJiZhZtMNqU5xzVFdXU1ZWxvr168nPz291Yq3yDxEREZEOqKSkhKysLLKzs0lKSlJC3QgzIykpiezsbLKysigpKWn1tZRUi4iIiHRAu3btIiMjI9phtBsZGRns2rWr1ecrqRYRERHpgGpra0lMTIx2GO1GYmJiUHXnSqpFREREOiiVfLRcsJ+VkmoRERERkSBFNKk2s0fNrMjMvmhiv5nZ/5rZSjNbbGYjIxmfiIiIiEhrRHqm+nHglGb2fwcY5HtMBf4cgZhEREREpJ279957OeeccygoKMDM6NevX0THj2ifaufcXDPr18whE4EnnXMOmGdmXcysh3Nuc0QCDIBzjtK91XRKiic5IT7a4YiIiIjEtJtuuomuXbsycuRIdu7cGfHx21pNdS9gg9/rQt+2Nuf9lds57I7XWbQ+8t80EREREfmmVatWsX37dl5//XV69uwZ8fHbWlLd2G2XrtEDzaaa2QIzW1BcXBzmsPaXl+mttrOlrCLiY4uIiIjINxUUFER1/LaWVBcCffxe9wY2NXagc+4R59wo59yonJyciATnLy+zEwCbS5VUi4iIiMS6tpZUvwRc5OsCMgYobYv11ABpyQmkJyewRUm1iIiISMyL6I2KZvZ3YByQbWaFwK1AIoBz7i/AbOBUYCWwB7g0kvEFKi8zRUm1iIiItDu3v7yEpZvKoh3GNxzUM4NbTz842mG0WqS7f5x/gP0O+FGEwglaXmYKm1VTLSIiIhLzIppUdzR5GSms2Br5myRFREREgtGeZ4TbqrZWU92u9MhMoXhXJTW1ddEORURERESiSEl1EPIyO1HnoLi8MtqhiIiIiEgUqfwjCPW9qjeXVtDD12JPRERERCLvqaeeYt26dQAUFxdTVVXFXXfdBUDfvn2ZMmVKWMdXUh2EvAwvkVYHEBEREZHomjFjBnPmzPnGtltuuQWAsWPHKqluy3pkpgBaAEZEREQk2t55552ojq+a6iB06ZxIckIcW9VWT0RERCSmKakOgpl5vao1Uy0iIiIS05RUBykvI4UtpXujHYaIiIiIRJGS6iD1yExhi8o/RERERGKakuog5WV2YmtpJXV1LtqhiIiIiEiUKKkOUl5GMlW1dZTsqYp2KCIiIiISJUqqg5Sb4bXVKyrTqooiIiIisUpJdZC6Z3irKhbtUl21iIiISKxSUh2k3HTfTPUuzVSLiIiIxCol1UHKSfdmqouVVIuIiIjELCXVQUpJjCcjJUGrKoqIiIjEMCXVIZCbkaIbFUVERERimJLqEMhNT9aNiiIiIiIxTEl1CHhJtWaqRURERKJhxYoVTJs2jTFjxpCTk0N6ejqHHXYYd999N7t3745IDEqqQyA3I4WiXZU4p1UVRURERCLt0Ucf5YEHHmDAgAFMmzaN3/72twwZMoRf/epXHHPMMezduzfsMSSEfYQYkJueTFVNHWV7a8jsnBjtcERERERiytlnn82NN95IZmbm19uuuuoqBg0axN13382MGTO45pprwhqDZqpDoL6tnuqqRURERCJv1KhR30io65177rkAfPHFF2GPQUl1CGgBGBEREZG2p7CwEIDu3buHfSwl1SGQq6XKRURERNqU2tpa7rjjDhISErjgggvCPp5qqkMgt778Q72qRUREpD34zy9hy+fRjuKb8g6B79wXssv99Kc/Zd68edxzzz0MGTIkZNdtimaqQyAtOYFOifEq/xARERFpA2655RYefPBBpk6dyo033hiRMTVTHQJmRm6GelWLiIhIOxHCGeG25rbbbuOuu+7i0ksv5S9/+UvExtVMdYjkpidTVKaaahEREZFouf3227n99tu56KKLmD59OmYWsbGVVIdIbkYKxZqpFhEREYmKO+64g9tuu40pU6bw2GOPERcX2TRX5R8hkpuezBwl1SIiIiIR99BDD3HrrbeSn5/PSSedxDPPPPON/d27d+db3/pWWGNQUh0iuekplFfWsKeqhs5J+lhFREREImX+/PkArF+/nosvvni//WPHjg17Uq3yjxBRWz0RERGR6Hj88cdxzjX5eOedd8Ieg5LqENm3AIySahEREZFYo6Q6RPYtVa4OICIiIiKxRkl1iKj8Q0RERCR2KakOkS6dE0mKj2OrZqpFREREYo6S6hAxM3LSk9WrWkRERCQGKakOoWwl1SIiIiIxSUl1COUqqRYRERGJSUqqQygnPVkt9URERERikJLqEMpNT6ZkdxXVtXXRDkVEREREIkhJdQjV96reVq7ZahEREZFYoqQ6hHJ8vapVVy0iIiISW5RUh5AWgBERERGJTUqqQ+jrmWqVf4iIiIjEFCXVIZSdpplqERERkUhbvnw53//+9xk2bBiZmZl07tyZoUOHct1117F58+aIxJAQkVFiRFJCHFmdEynSUuUiIiIiEVNYWMjmzZs588wz6d27NwkJCXz++ec88sgjzJo1i0WLFpGbmxvWGJRUh1hueopuVBQRERGJoAkTJjBhwoT9tp9wwglMnjyZxx9/nOuvvz6sMaj8I8RyM7QAjIiIiEhb0LdvXwB27NgR9rE0Ux1iOWnJrC7eHe0wRERERGJORUUF5eXlVFRUsHTpUm644QYATj311LCPrZnqEMvJSKZ4VyXOuWiHIiIiIhJTpk+fTk5ODn369OHkk09m586dzJw5k+OPPz7sY2umOsRy0pKpqq2jdG81XTonRTscERERkf38+uNf82XJl9EO4xuGdh3KDaNvCOoaZ5xxBkOHDqW8vJxPP/2Ul156ieLi4hBF2Dwl1SGWm+EtVV68q1JJtYiIiEgE9e7dm969ewNegn3WWWdx5JFHsnfvXm688cawjq2kOsRy6ntV76pkUPf0KEcjIiIisr9gZ4TbixEjRnD44Yfz8MMPhz2pVk11iOVm+FZVVAcQERERkajbu3cvJSUlYR9HSXWI5abXz1RrARgRERGRSNiyZUuj299++22++OILxowZE/YYVP4RYmnJCaQkxmmmWkRERCRCfvjDH7J582ZOPPFE+vbtS0VFBZ988gmzZs0iPT2d3/3ud2GPQUl1iJkZuekpWgBGREREJELOP/98nnjiCZ566imKi4sxM/r27cuVV17JL37xC/Lz88Meg5LqMMhJT6aoTEm1iIiISCRMnjyZyZMnRzUG1VSHQW56MsXlSqpFREREYoWS6jDITU+mqEw3KoqIiIjECiXVYZCTnkxZRQ0V1bXRDkVEREREIkBJdRjkpu9bVVFEREREOj4l1WGQ4+tVrbpqERERkdigpDoM6pNqdQARERERiQ1KqsOgflXFYq2qKCIiIhITlFSHQbe0ZOJMNdUiIiIisUJJdRjExxnd0pK1qqKIiIhIjFBSHSY5acmaqRYRERGJERFPqs3sFDNbbmYrzeyXjezPN7O3zexTM1tsZqdGOsZQyM3QTLWIiIhIrIhoUm1m8cBDwHeAg4DzzeygBof9CnjOOXc4cB7wcCRjDJWctGSKdKOiiIiISEyI9Ez1aGClc261c64KmAVMbHCMAzJ8X2cCmyIYX8jkZiSzrbyKujoX7VBEREREJMwinVT3Ajb4vS70bfN3G3ChmRUCs4FrIxNaaOWkJVNb5yjZUxXtUERERERizp49e+jfvz9mxjXXXBP28SKdVFsj2xpO5Z4PPO6c6w2cCjxlZvvFaWZTzWyBmS0oLi4OQ6jByc3QUuUiIiIi0TJt2jS2bdsWsfEinVQXAn38Xvdm//KOy4HnAJxzHwIpQHbDCznnHnHOjXLOjcrJyQlTuK1XvwCMblYUERERiayFCxfyhz/8gdtvvz1iY0Y6qZ4PDDKz/maWhHcj4ksNjlkPTAAws2F4SXXbm4o+gJyvV1VUUi0iIiISKbW1tVxxxRWccsopTJo0KWLjJkRsJMA5V2Nm1wCvAvHAo865JWZ2B7DAOfcS8DPgb2b2P3ilIZc459rd3X45X89UqwOIiIiISKQ88MADfPnllzz//PMRHTeiSTWAc2423g2I/tum+X29FDg20nGFWuekBNKSEygq00y1iIiISCSsWbOGW2+9lWnTptGvXz/Wrl0bsbEjnlTHktz0ZIrLlVSLiIhI27LlnnuoXPZltMP4huRhQ8m76aagrvHDH/6Q/v37c91114UoqpZTUh1G2enJFGumWkRERCTsZs6cyWuvvcbcuXNJTEyM+PhKqsMoNz2ZJZvKoh2GiIiIyDcEOyPc1lRWVnLddddx6qmnkpeXx8qVKwHYuHEjAKWlpaxcuZLs7Gy6dOkSlhgi3f0jpuSmp1BUphsVRURERMJp7969FBcX88orrzBo0KCvH+PGjQO8WexBgwYxffr0sMWgmeowyklPZndVLbsra0hN1kctIiIiEg6pqan84x//2G97cXExV199NaeccgqXX345I0aMCFsMyvTCKNevV7WSahEREZHwSExM5Oyzz95ve333jwEDBjS6P5RU/hFGOVpVUURERCQmaPo0jHIztKqiiIiISLT069ePSK0hqJnqMMpJ06qKIiIiIrFASXUYZXVOIiHONFMtIiIi0sEpqQ6juDgjJz1ZNdUiIiIiHZyS6jDLSU/WTLWIiIhIB6ekOsxyNVMtIiIi0uEpqQ4zb6ZaNyqKiIiIdGRKqsMsJz2F7burqK6ti3YoIiIiIhImSqrDLC8jBefUq1pERESkI1NSHWZ5mV6v6i1lKgERERER6aiUVIdZ94wUALaWKqkWERER6aiUVIdZj8xOAGxWUi0iIiLSYSmpDrOszokkJcSxVeUfIiIiIh2WkuowMzPyMlJUUy0iIiLSgSmpjoC8jBSVf4iIiIiEkZk1+khLS4vI+AkRGSXGdc9MYXHhzmiHISIiItKhHX/88UydOvUb2xITEyMytpLqCOiRmcJrSypwzmFm0Q5HREREpEMqKCjgwgsvjMrYKv+IgO4ZKVTW1LFzT3W0QxERERHp0KqqqigvL4/4uEqqIyDP16taNyuKiIiIhM8///lPOnfuTHp6Orm5uVx77bWUlpZGZGyVf0RAXua+pHpYj4woRyMiIiLS8YwePZpzzjmHgQMHUlZWxuzZs3nwwQeZM2cOH3zwQdhvWFRSHQFfJ9XqACIiIiJtwLvPrWDbhsiXSDQnu08ax08e3OrzP/roo2+8vuiiixgxYgQ333wzf/zjH7n55puDDbFZKv+IgNz0ZMyUVIuIiIhE0i9+8QuSkpJ45ZVXwj6WZqojIDE+juy0ZK2qKCIiIm1CMDPC7UliYiI9e/Zk27ZtYR9LM9URogVgRERERCKroqKCwsJCunfvHvaxlFRHSPeMFM1Ui4iIiITB9u3bG91+yy23UFNTw+mnnx72GFT+ESE9MlNYsK4k2mGIiIiIdDh33XUX8+bNY/z48eTn51NeXs7s2bN5++23Oeqoo7j22mvDHoOS6gjJy0xh555qKqprSUmMj3Y4IiIiIh3GuHHjWLp0KU888QTbt28nPj6eQYMGcffdd3PdddeRkpIS9hiUVEfI1wvAlFbQLzs1ytGIiIiIdBwTJ05k4sSJUY1BNdUR4r8AjIiIiIh0LEqqI6R7hhaAEREREemolFRHSA/fTLXa6omIiIh0PEqqIyQ1OYHMTols2rk32qGIiIiISIgpqY6gXl06sVFJtYiIiEiHo6Q6gnp26aSZahEREZEOSEl1BPXO6sTGHUqqRURERDoaJdUR1KtLJ3ZV1lBWUR3tUEREREQkhJRUR1DPLp0ANFstIiIi0sEoqY6gXllKqkVEREQ6IiXVEdSzi9erelOpkmoRERGRjkRJdQRlpyaTlBCnmWoRERGRDkZJdQTFxRk9M1PUq1pERESkg1FSHWG9srQAjIiIiEg4lJSU8POf/5yBAweSkpJCTk4O48eP59133w372AlhH0G+oWdmJ9Bc2iMAACAASURBVOasKI52GCIiIiIdyrp16xg3bhzl5eVcfvnlDB48mNLSUhYvXszGjRvDPr6S6gjrldWJol2VVNbUkpwQH+1wRERERDqECy+8kJqaGhYvXkyPHj0iPr7KPyKsl69X9ZbSiihHIiIiItIxzJ07l/fee4/rr7+eHj16UF1dzZ49eyIag5LqCOulBWBEREREQmr27NkA5Ofnc/rpp9OpUydSU1MZPHgwM2fOjEgMSqojrE/XzgCsL4nsb08iIiIiHdXy5csBuOKKKygpKeGJJ55gxowZJCUlMWXKFB577LGwx6Ca6gjrkZlCQpwpqRYREZGoefvxRyhatzraYXxDbt8Cxl8ytVXn7tq1C4D09HTefvttkpKSADjzzDMpKCjgpptu4uKLLyYuLnzzyZqpjrCE+Dh6Z3VinZJqERERkZDo1Mkrrz3//PO/TqgBsrKy+N73vseWLVu+ns0OF81UR0Gfrp3ZoKRaREREoqS1M8JtVe/evQHIy8vbb199J5AdO3aENQbNVEdB326dWbddSbWIiIhIKIwePRqAwsLC/fbVb8vNzQ1rDEqqoyC/a2dK91ZTuqc62qGIiIiItHtnnHEG6enpzJw5k/Ly8q+3b968mX/9618MGjSIgQMHhjUGJdVRkN81FVAHEBEREZFQyMrK4v7772fjxo2MGTOG3//+99x3332MGTOGqqoqHnzwwbDHoJrqKOjbzWurt65kN4f0zoxyNCIiIiLt39SpU8nOzuY3v/kNt9xyC3FxcRx99NE888wzHHvssWEfX0l1FKhXtYiIiEjoTZo0iUmTJkVlbJV/REFacgLZaUms182KIiIiIh2Ckuoo6dO1s2aqRURERDoIJdVR0rer2uqJiIiIdBRKqqMkv2tnNpfupaqmLtqhiIiIiEiQlFRHSd9uqdQ53awoIiIi0hEoqY6SAblpAKwuLj/AkSIiIiLS1impjpKCHG8BmFXFu6MciYiIiIgES0l1lGSkJJKbnswqzVSLiIiItHsRT6rN7BQzW25mK83sl00cM9nMlprZEjN7JtIxRsqAnDQl1SIiIiIdQESTajOLBx4CvgMcBJxvZgc1OGYQcCNwrHPuYOCnkYwxkgbkprKqqBznXLRDEREREZEgRHqmejSw0jm32jlXBcwCJjY45grgIefcDgDnXFGEY4yYguw0yipq2L67KtqhiIiIiEgQIp1U9wI2+L0u9G3zNxgYbGbvm9k8MzslYtFFWH0HkFVFKgERERERac8inVRbI9sa1j4kAIOAccD5wHQz67LfhcymmtkCM1tQXFwc8kAjYYA6gIiIiIh0CAmBnmBmBcBkIB9IabDbOecub+b0QqCP3+vewKZGjpnnnKsG1pjZcrwke36DgR4BHgEYNWpUuyxK7pnZiZTEON2sKCIiIhKE2267jdtvv73J/QkJCVRXV4c1hoCSajObCPwDb4a7CKhscMiBktv5wCAz6w9sBM4DLmhwzL/wZqgfN7NsvHKQ1YHE2V7ExRkF2eoAIiIiIhKMSZMmMXDgwP22L168mN/+9recfvrpYY8h0Jnqu4B3gO875wKuuXDO1ZjZNcCrQDzwqHNuiZndASxwzr3k2/dtM1sK1AK/cM5tD3Ss9mJAbhqfrt8R7TBERERE2q0RI0YwYsSI/bZfeeWVAFx+eXOFFKERaFJdAPysNQl1PefcbGB2g23T/L52wHW+R4c3ODeNlz/bRHllDWnJAVfjiIiIiEgj9uzZw6xZs+jVqxennBL+vheB3qj4JdAtHIHEqoN6ZgDw5eayKEciIiIi0nE899xzlJWVcemllxIfHx/28QJNqq8HbvLdrCghMKyHl1QvVVItIiIiEjIzZszAzLjssssiMl6g9Qa34c1ULzOzr4CSBvudc25sKAKLFT0yU+jSOZFlSqpFREQkQna+vIqqTW2rpW9Sz1S6nD4gJNdavnw57733HhMmTKB///4hueaBBJpU1wLLwxFIrDIzhuVlsHSTkmoRERGRUJgxYwYAP/jBDyI2ZkBJtXNuXJjiiGkH9cxg5rx11NTWkRAf6fV4REREJNaEaka4LaqpqeHJJ5+ka9eunHnmmREbVxlcGzCsRwaVNXWs3d62/gwjIiIi0t68/PLLbN26lSlTppCcnByxcQNOqs2sh5ndb2bzzWyVmX1sZr8xs7xwBBgLDvr6ZsVdUY5EREREpH2rL/2IRG9qfwEl1WY2GFgE/BgoBz4GdgM/ARaZ2aCQRxgDBuamkRhvqqsWERERCcKmTZv473//y+jRoznkkEMiOnagNyr+GigDjnLOra3faGZ9gdd8+yeFLLoYkZQQx8DcdLXVExEREQnC448/Tm1tbURvUKwXaPnHeOAW/4QawDm3Dq/d3vjQhBV7RvTK5LMNO/EWlBQRERGRQN10000457jiiisiPnagSXUS0FTh7y7ffmmFkX27ULq3mjXbdLOiiIiISHsTaFK9CLjWzL5xnpkZcLVvv7TC4flZAHy6fmeUIxERERGRQAVaU30H8G+8FRWfBTYDecA5wCDgu6ENL3YMzEkjPTmBTzfs4Kwjekc7HBEREREJQKCLv/zXzE4D7gJuBgxwwCfAac6510IfYmyIizMOy++imWoRERGRdijgPtXOuf8650YB6UAfIN05N9o592rIo4sxh+dnsWxzGbsqqqMdioiIiIgEoNUrKjrn9jjnNjrn9oQyoFg2pqArdQ7mry2JdigiIiIiEoADln+Y2TRgunNuk+/r5jjn3J2hCS32jMzPIikhjg9WbufEod2jHY6IiIiItFBLaqpvA/4LbPJ93RwHKKlupZTEeI7Iz+LD1dujHYqIiIh0AM45vCZtciDBrhVywPIP51ycc+5jv6+be8QHFY1w9IBuLN1cxo7dVdEORURERNqxpKQk9u7dG+0w2o29e/eSnJzc6vMDqqk2s3wzS2xiX4KZ5bc6EgHg2IHZOAfvrtwW7VBERESkHcvOzqawsJCSkhKqq6u1anMjnHNUV1dTUlJCYWEh3bp1a/W1Au1TvQY4Gvi4kX2H+rZrtjoIh/XpQrfUJN5YupXvHdoz2uGIiIhIO5WZmUlycjLFxcVs376dmpqaaIfUJiUkJJCSkkJ+fj4pKSmtv06AxzdXlJMI1LU6EgEgPs4YPzSX15Zsobq2jsT4VjdoERERkRiXkpJCnz59oh1GTGhJ948uQFe/Tb3MrKDBYZ2Ai4EtIYwtZp00LJd/flLI/LUlHDMgO+zjVdbU8tmGUpZsKmV7eRXVtXVkdk6kX7dURvXNIjej9b+1iYiIiMSClsxU/wS4Fa+zhwP+2cRx5jtOgnT8oBxSEuN4ZfHmsCbVn6zbwdPz1jH7i81UVHt/ZIiPM+LjjKqafX90GN4rg0mH9+bsUb3JSGm0pF5EREQkprUkqf4XsBYvaX4Ub4nyVQ2OqQSWOucWhzS6GJWanMDJB+fx78WbmXb6QSQnhLZM/cstZdw7+0vmrCgmLTmBSSN7M25wDofnZ9EtNYm4OGNPVQ0rtpbz8ZrtvPzZZu7491L+8MYKLj+ugCtO6E/npEArh0REREQ6LgvkTlAzuxj4t3OuTTVSHjVqlFuwYEG0wwipOSuKufjRj/nLhSM5ZXiPkFyzqqaOB9/6iofeWUVqUjzXnDiQC8f0bVGC/HlhKf/71le8vnQrvbM6cefE4YwfmhuSuERERETaCzP7xDk3ar/tHaG9SkdMqmtq6zjmvrcY1iODJy4bHfT1Cnfs4YczF/L5xlImjezFtNMOokvnpICv89Hq7dz8ry9YWVTOmYf34s4zhpOWrFlrERERiQ1NJdUBZ0NmNhy4HBgCNLyDzTnnJrQuRPGXEB/HRUf35f7XVrB8yy6G5KW3+lofrNrGNc98SnVNHX+dcgQnH5zX6msdVdCN2T8+nofeXsmf3vqKRRt28uAFh3Nwz8xWX1NERESkvQt08ZejgAXAd4CTgSygABgHDKT5lnsSoO8f1ZdOifE8Mnd1q853zjH93dVMmfExXVOTePGaY4NKqOslJcTxP98azN+vGMOeqhrOfPgDXly0MejrioiIiLRXgTZBvgd4ATgYL4G+3DnXDzgJb9GXu0IaXYzLSk3igqPy+b9PC1m2uSygc/dW1fLTZxdx1yvL+Naw7vzrR8dSkJMW0vjqZ60P69OFn8xaxP2vLqeurv2XE4mIiIgEKtCkegQwE6+1HvhWT3TOvYWXUN8butAE4NoTB5LZKZHbXlrS4oR17bbdnPnw+7z02SZ+cfIQ/nzhyLDVPXdLS2bm5Udx7qg+PPj2Sq5+eiF7q2rDMpaIiIhIWxVoUp0I7HbO1QElgH9biuXA8FAFJp4unZO44ZShfLSmhD/PadjJcH+vLdnC6X96jy1lFTx2yZH8aPxAzMJblZOUEMd9Zx3Cr747jFeXbmHKjI/YuacqrGOKiIiItCWBJtWrgF6+rxcDl5lZnJnFAZeiFRXD4twj+zDxsJ7c/9pynp2/vtFjtpdXct2zi5j61Cf0y07l5WuOY9yQyLW8MzN+cHwBD54/ksWFpZzzlw/ZXLo3YuOLiIiIRFOgNQEv492U+AxeffUrQBlQC6QBPw5lcOIxM+6bNIKS3VXc8PznvL9yOxcd3ZfeWZ3ZuHMPry7Zyt8/Wk9FTS0/PnEgPzpxYMgXjGmp747oQVZqIlOf/ISzHv6AJy8fzcDc1ncuEREREWkPgupTbWaHA2cBnYH/OudeC1VggeiIfaobU11bxx/eWMGj761lb/W+uuU4g+8c0oOfTBjE4O5tI4H9YmMplzw2n5q6OmZcfCRH9M2KdkgiIiIiQdPiLx3Ijt1VzF9bQtGuSrLTkhlT0LVVC7mE2/rte7jo0Y/YUlbBQxeMZMKw7tEOSURERCQoSqolKraVV3LpY/NZurmMu88Yznmj86MdkoiIiEirtXpFRTNbw74WegfinHMDAg1OOq7stGRmTR3DD59eyC9f+JytZZX8eEL4O5KIiIiIRFJLblScQ8uTapH9pCYnMOPiUfzy+c954I0VbCnby50Th5MQH2jzGREREZG26YBJtXPukgjEIR1cYnwc958zgrzMZB56exXFuyr50/kj6ZQUnS4lIiIiIqGkqUKJGDPjFycP5c6JB/Pml0VcMH0eJbu1SIyIiIi0fwH1qTaziw50jHPuydaHI7FgytH9yElP4SezPuXMh9/nbxeNajOtAEVERERaI6DuH2ZW18Sury/inIv43/PV/aN9Wrh+B1c+9Ql7Kmt44NzD+PbBedEOSURERKRZTXX/CLT8o38jj1HA7cBXwFFBxikxZGR+Fi9fcxwDc9OY+tQn/OnNr+gILR5FREQk9gRU/uGcW9fI5nXAQvN6pF0HXBCKwCQ25GWm8OyVR3PjC5/zu9dXsHRzGb8+ewQZKYnRDk1ERESkxUJ5o+K7wHdDeD2JESmJ8fx+8qHcfOowXlu6ldP+9z0+27Az2mGJiIiItFgok+oxQHkIrycxxMy44oQCnrtyDLV1jrP+/AF/m7uaujqVg4iIiEjbF2j3j2mNbE4ChuPNUj8YiqAkdh3Rtyuzf3w81z//GXfPXsbcr4q576wR9OrSKdqhiYiIiDQpFN0/KvHqqmcB9zrnKkMUW4up+0fH45zj6Y/Wc8/sZcSZcfN3h3HekX20vLmIiIhEVVPdPwK9UVGLxUhEmBkXjunL2ME5XP/Pxdz4wufM/nwzd04cTr/s1GiHJyIiIvINSpKlTevTtTNP/+Ao7jpjOAvX7eDbD8zld68tZ29VbbRDExEREflaQOUfAGYWD1wEHA30AjYCHwBPOeeikumo/CM2bC2r4N7Zy/jXok306tKJW04bxskH56kkRERERCImJIu/mFlfYAkwAzgFyPU9Pwp84dsvEhbdM1L4w3mH8+zUMaSnJHDVzIWc98g8Fq7fEe3QREREJMYFWv7xIJABHOecy3fOHemcyweOBzKBP4U6QJGGjiroxr+vPY47Jh7MquJyJj38AVOfXMDKol3RDk1ERERiVKDdP3YDVzvnnmhk3yXAg865tNCF1zIq/4hduytrmPHeGh6Zu5o9VTWcNbI3P54wiD5dO0c7NBEREemAQlL+gbe4S1ET+4qAPYEGJhKM1OQEfjxhEHN+MY5Lj+3Pi4s2Mf7+d/jFPz5j7bbd0Q5PREREYkSgM9W/AwY65yY2su9F4Cvn3M9DGF+LaKZa6m0u3ctf56zm7x+vp7q2ju8d2pNrThzIwNz0aIcmIiIiHUBTM9WBJtU/BG4ESoHnga1Ad+BsIB24F6iqP94592hwYbeMkmppqGhXBdPfXcPMeevYW13Ld4bncfW4gQzvlRnt0ERERKQdC1VS3diKik1xzrn4AI5vNSXV0pSS3VU8+t4anvhgLbsqazh+UDZXjR3AMQO6qRWfiIiIBCxUSXVALfOcc+sCOb61lFTLgZTurebpj9bx6Htr2VZeySG9Mrlq7ABOGZ5HfJySaxEREWmZkCTVbZWSammpiupaXli4kUfmrmLt9j3069aZK04o4KyRvUlJjMgfVkRERKQdC2lSbWbDgbFAV2A7MNc590XQUbaSkmoJVG2d49UlW/jLnFUsLiwlOy2ZS4/tx4Vj+pLZKTHa4YmIiEgbFaryjwTgceB8wP9v5g54BrgkGkuVK6mW1nLO8eHq7fxlzmrmrigmNSmeC47K5/LjCsjLTIl2eCIiItLGNJVUJwR4nVuBycA0YCawBcgDLvTtW+17FmkXzIxjBmRzzIBslmwq5a9zVjPjvTU8/sFazjisF1eOLVA7PhERETmgQGeq1wCPOufubGTfNOBS51z/EMbXIpqpllDaULKHv727mucWbKCiuo5vHdSdq8YO4Ii+WdEOTURERKIsVOUflcB3nXNvNLLvJOAV51xyUJG2gpJqCYft5ZU88cFanvhwHaV7qzmyXxZXjR3A+CG5xKljiIiISEwK1TLlm4Bjm9h3jG+/SIfQLS2Z6749hA9+eSLTTjuIjTv2cvkTCzjlj3N5/pNCqmsDadsuIiIiHVmgSfXTwM1mdouZFZhZJzPrb2Y3AjcDT4U+RJHoSk1O4LLj+jPn+vH8fvKhGMbP/vEZY3/zNjPeW8PuyppohygiIiJR1pruH08C5+F1/Ph6F/B34CJ1/5COzjnH28uL+Ms7q/l4bQmZnRK56Oi+XHxMP7LTIl79JCIiIhEUqprqbKAcGACcgNenugSY45xbGqJYA6akWqLlk3U7+OucVby+bCtJ8XGcM6o3VxxfQN9uqdEOTURERMKg1Um1mcUDtwA/BdKBWuBl4HLn3M5WBHIK8EcgHpjunLuviePOBv4BHOmcazZjVlIt0bayqJzp767mhYUbqamr4zvDe3DV2AEc0jsz2qGJiIhICAWTVP8I+BPwDjAfKADOBJ5yzl0aYBDxwArgW0Ch73rnN5zlNrN04BUgCbhGSbW0F1vLKnjs/bU8PW8duyprOGZAN64aO4DjB2Vjpo4hIiIi7V0wSfUi4CPn3JV+264EHgRSnXNVAQRxNHCbc+5k3+sbAZxz9zY47g/AG8DPgZ8rqZb2pqyimr9/tJ4Z762haFclB/XI4MqxBXz3kB4kxAd6f7CIiIi0FcG01CvAK8Pw9yxe+UbfAOPoBWzwe13o2/Y1Mzsc6OOc+3eA1xZpMzJSErly7ADevWE8vzlrBJU1tfxk1iLG3f8OT3ywlj1V6hgiIiLSkbQkqU4Dyhps2+V7DnT95sb+/v31VLmZxQEPAD874IXMpprZAjNbUFxcHGAYIpGRnBDP5CP78Pr/jOWRKUeQm57MrS8t4dj73uKB11dQsrvFf+gRERGRNqwl5R91wFnAZ36b44HlwERgif/xzrnVzVyr2fIPM8sEVuF1GAHIw+su8r3mSkBU/iHtyfy1Jfx1zireWFZESmIck0f14dJj+9M/Wx1DRERE2rpgaqrr+GZP6q93NbbdORffzLUS8G5UnABsxLtR8QLn3JImjn8H1VRLB7Vi6y7+Omc1L322kZo6x4lDcrnsuP4cM6CbbmoUERFpo5pKqhNacG5AHT6a45yrMbNrgFfxZrsfdc4tMbM7gAXOuZdCNZZIWze4ezq/m3woN3xnCDPnrefpeev4/vSPGNI9ncuO68fEw3qRktjk76giIiLShgS0+EtbpZlq6Qgqqmt5+bNNPPr+WpZtLqNrahIXjM5nytF96Z6REu3wREREhBCtqNhWKamWjsQ5x7zVJTz6/hreWLaVeDNOG9GDS47tz6G9M1UaIiIiEkXBlH+ISASZGUcP6MbRA7qxbvtunvhgHc8t2MC/Fm3ikF6ZXDgmn+8d2otOSSoNERERaSs0Uy3SDpRX1vB/n25k5ofrWL51FxkpCZx1RG8uHNOXATlp0Q5PREQkZqj8Q6QDcM6xYN0OnvpwHf/5YjPVtY5jBnRjypi+nHRQdxK1WqOIiEhYKakW6WCKd1Xy3IINPPPRejbu3EtuejLnj87n3CP70LNLp2iHJyIi0iEpqRbpoGrrHO8sL+KpeeuYs6IYA04YnMN5R/ZhwjDNXouIiISSkmqRGLChZA//WLCB5xYUsqWsguy0JM4a2ZvJR/ZR7bWIiEgIKKkWiSG1dY65K4qZNX89by4roqbOMbpfV849sg+nHtJDnUNERERaSUm1SIwq2lXBCws38uz8DazZtpv05AQmHt6T847MZ3ivzGiHJyIi0q4oqRaJcc45Pl5TwrPzN/DK55uprKljaF46Z43szcTDe5KbrlUbRUREDkRJtYh8rXRvNS8t2sg/F27ksw07iY8zThiUzVlH9OakYd1JSVR5iIiISGOUVLdXNVWw8AlY9TYkJEP+GDj8QkhKjXZk0kGsLCrnhYWF/N+nG9lcWkF6SgKnjejJ2Uf0YmR+lpZFFxER8aOkuj3auR6eOQ+KlkC3gVBbDTvXQVp3OGs69D8h2hFKB1Jb5/hw1XaeX1jIf7/Ywt7qWvpnpzLp8F6cObIXvbM6RztEERGRqFNS3d7s3gaPngy7i+HMv8KQ73jb138EL10L21fCGX+GQ8+NbpzSIZVX1vCfzzfz/MJC5q0uAWBMQVcmHd6bk4fnkdkpMcoRioiIRIeS6vZm1vdh5Rtw0YteyYe/yl3w9/Nh3Qdw7kwYemp0YpSYULhjD/+3cCMvfLqRNdt2kxQfx/ihOUw8rBcnDs1V/bWIiMQUJdXtyZevwKwL4KTb4Lj/afyYynJ44jTYvgqmvgPdBkQuPolJzjkWF5by4qJNvLx4E8W7KklPTuDk4XlMPKwnRxd0I0GrN4qISAenpLq9qKuFh46CuAS46l2Ib+bP7DvXw19PgIxe8IM3ILFT5OKUmFZb55i3ejsvLtrIfz7fwq7KGrLTkjltRA8mHtaTw/p00Q2OIiLSISmpbi+WvgjPXQRnPwbDJx34+K/egKfPgqN+CN+5L/zxiTRQUV3LO8uLeHHRJt78soiqmjryu3Zm4mE9mXhYTwbmpkc7RBERkZBRUt1ePDIeKnbCNQsgroW1qq/8HOZPh8tehfyjwhufSDPKKqp59YstvPTZJt5fuY06B0Pz0jn1kB6cekgPBuamRTtEERGRoCipbg+2fA5/OQ5O+TWMuarl51XugoeP9so/rnrP62ctEmVFuyp4ZfFmZn++mflrdwBKsEVEpP1TUt0e/Pcm+PgR+NlySO0W2Ln1ZSATpsHxPwtPfCKttKW0gv98oQRbRETaPyXVbV1tNfx+GPQ5Cs57unXXmPV9b+XFaxdARs/QxicSIkqwRUSkPVNS3datngNPfg8mPwUHfa911yhZ43UOOfgMmPRIaOMTCYOmEuxvH5zHyQd356AeGeoiIiIibYqS6rbuPzfAJ4/D9ashKbX113nzDnj3d3D569BndMjCEwm3+gT7P59vYf66EpyD3lmdOPngPL59UHdG9etKfJwSbBERiS4l1W2Zc/DHEZB7EFzwbHDXqiyHB0dBWne44m2I02Ic0v5sK6/kzWVbeXXJVt77ahtVtXV0S03ipGHdOXl4d44ZkK2VHEVEJCqaSqoTohGMNFC01FvI5fifB3+t5DT41h3wwhWw6GkYOSX4a4pEWHZaMucemc+5R+ZTXlnDO8uLeHXJVl75fDPPLthAalI844bm8u2DujN+aC4ZKc0skiQiIhIBSqrbgpVveM+DTw7N9Q45x+si8tadXn11shbfkPYrLTmB00b05LQRPamsqeXDVdt5dclWXl+6lVcWbyYx3jh6QDYnDcvlxKG59M7qHO2QRUQkBqn8oy2YeRaUFsKPPgrdNTfMhxknebPfE24J3XVF2ojaOsen63fw6pItvLGsiDXbdgPejY4nDs1lwrBcDuuTpTpsEREJKdVUt1U1VfDrvnD4FDj1N6G99vM/gKUveS32uuSH9toibczq4nLe+rKIN5ZtZf7aHdTWObqmJjFuSA4ThnbnhMHZpKtMREREgqSa6rZq4ydQvQf6nxD6a590Gyz7N7x+K5zzWOivL9KGFOSkUZCTxg+OL6B0bzVzVxTz5rKtvPVlES8s3EhCnHFUQVdOHNqdCUNz6ZcdRJcdERGRBpRUR9uauYBBv2NDf+3M3nDsj2HOr+GoKyF/TOjHEGmDMjslcvqhPTn90J7U1Nbx6YadvLmsiDeXbeXOfy/lzn8vZUBOKuOG5DJ2cA6j+3dVNxEREQmKyj+i7alJUL4Vfvh+eK5ftRv+dASk94AfvKkWexLz1m/fw1tfbuXNL4v4aE0JVTV1pCTGMaagG2MH5zB2cA79s1O16IyIiDRK5R9tUV2dV/5x0MTwjZGUChNuhX9dBZ8/B4eeF76xRNqB/G6dueTY/lxybH/2VtUyb8125iwvZu6KYm5/eSkAfbp28iXYuRw9oBtpyfpPpYiINE//p4imklVQsRN6HxnecUacCx//Fd64DYadHtyKjSIdSKekeMYPyWX8kFzAm8We81Uxc5YX88LCwHBKdgAAIABJREFUjcyct57EeGNU366MHeLNYg/NS9cstoiI7EflH9G06O/eDPLV8yB3WHjHWj8PHj0Zxt4A428K71giHUBVTd3/s/feQZZd+WHed+PLsXOY7p7uyQkzgzDYATDALrDkLsVdcoN3KWq5FEGRJZF2kXRJrpLlcrFkSabsP0zKMmWpZFGWZFImKapI0aJILnYBDIAdhAEGk3Po6Zy7X794373Hf5z7UndPANBx5nxVp865554bHtDT/fWvf/d3+eDODG9clZJ9eSwDQGsswPM7m3l+RzPP7WimLR7c4DtVKBQKxXqi0j82I0Pvgx2D5l1rf62eZ+HAN+Ct34SD34LmHWt/TYViC2ObOscHmjk+0Mzf/fJexhcKvHl1kjeuTvK6H8kG2NEarQr2sf60erujQqFQPKaoSPVG8s9PQDABP/uf1ud6mXH4p09DxyF5TfUnbIXiU+F5gktjC7xzfZq3rk/x3q0Z8o6LoWsc6k5UJftIT5KAqaqKKBQKxcPguA6LziKLziJZJ8tiabG2XcqScTLVecdz+PXjv74h96ki1ZuNUg7GL8Bzv7J+14y1wRd/Hf701+DM78KRv7Z+11YoHiF0XWN/Z4L9nQl+4UQ/xbLLR4NzvHN9ireuT/Hbr9/gf//+dYKWzjPbm3h+RxPHB5rZ1xFHV294VCgUjxiO55AtZasynCn58ussVsX4YbaLbvGB1zI1k4gdIWpF8YSHrm2eqmYqUr1R3Pkh/M6X4Kd+D/b82Ppd1/Pgd74MU1fgl9+DaOv6XVuheExYKDi8e3OGt33Jvj6xCEAqbHFsexPH+tM829/E7raYkmyFQrGhCCHIl/MslBbIlDLVtnQ74zTOVyLGWSdLwS088DqGZhC1o0StKBFLSnHUbhxX9sXsWG1+ybqAEdjwh8VVpHqzMfKR7LueXN/r6jp85bfgX7wIf/zL8NO/r9JAFIpVJh60+OK+Nr64rw2A8YUCb1+f4u3r07x7a5r/cmEMgGTY4th2KdhKshUKxaehIsX3kt/7irLfyqJ832uEzBAxK0bMli0dTNMb622UZH8ctaJE7AgxK1adj1gRgkZww2V4rVFSvVGMn4dIq0zJWG9a98AX/z782X8H7/9LeOYX1v8eFIrHiLZ4kK8f7ebrR7sBGJrN8e7NGU7dnObUrWn+/MI4ICX7mb6aZO9pV5KtUDwuuJ5LppRhvjTPfNFv/nihuLBsfqG4wHxx/qGkOGgEq0Ics2Okgil64j3E7Xh17l7jmBXDMtQD2A+DkuqNYvw8tO3fuOs/84tw7S/gL/4H6HtBirZCoVgXulNhup8M840npWQPz+V59+a0lOybM/zFRSnZiZDFM34k+9j2NHvaY5jG5skfVCgUy3Fcpya99SL8AEnOlDL3PW/UipIIJIjbcRKBBB2RDuJ2/KHE2Dbsdfr0jzcqp3ojcMvwjzplhPhH/+HG3UdmHP7ZcQg3wd/4HgTjG3cvCoWiyshcnndvTXPqxgynbk1zZzoHQMQ2ONKT4qm+FE/3pTm8LUlEve1RoVgzHM9hvjjPbGGWueLc8r44y1yh1s+X5sk62XueT0MjHoiTsBNSkOvGiUCiYVyR50QgQcyOYekqWrxZUDnVm4np6+AWof3gxt5HrA3+q38N/+Yn4I9+EX7qd2XOtUKh2FA6kyG+dqSbrx2RkezR+Tzv357lg9szvH97lt967RpCgKFr7O+M81Rvmqf6pGy3xtTLaBSKlfCEx0JxQQrwEkGeLcxW5+slOePcO3octaIkA0lSwRRNwSYGEgM1OV4iyAlbCnTMjm2qahWK1UVJ9UYwfl72G5n+UWH7C/Cl34A/+zvwF38PfvQfqQcXFYpNRkcixFefCPHVJzoBWV3kwzuznL4zy/u3Z/jd9+7wr96+BUBvU5inetM83Zfiqb40Ay2RR/7hIMXjiRCChdIC04VpZvIzzBSWt+n8dEMU2RPeiucKmSGSgWRVkrtj3aSCKbkdSJEMLukDSZVnrFiGkuqNYPwC6Ob6vEnxYXjmF2DmBpz6bQil4cW/s9F3pFAo7kM8aPHS7lZe2i1LYpbKHhdG5vngtpTsH1yZ4D98OATIMn5P9qY40pPiSE+SQ91JoiplRLFJKbrFqiBPF6aZzk+vKMuVNSs9oKehkQwkSQfTpENpdiZ3kgqmVpTkVDBFIpAgZIY24NMqHjXUd9aNYPwCNO8GM7DRdyLRNPjR/xkK8/CDfwAIOPF3VMRaodgi2KbuS3OKXzjRjxCCm1NZTt+e5b3bM3w4OMv3Lk0AoGuwqy1WleyjPUn6m6OqyohizSi6RabyU7LlZD+Zn1xRmu+Vjxw0gjSFmkgH07SH29nXtE9Kc12r7E8Gkpi60hvF+qO+6jaC8fPQ+9xG30Ujug5f/aeABj/4h7A4Dl/6x2CoLxGFYquhaRoDLVEGWqJ86+ltAMzlSpy5O8eHg3N8NDjLn54d4ffeGwQgHjQ53JPiyLYkR3qSHN6WJBlW1QIU98YTHvPF+Zog56er46pA+22lqhYaGqlgqirDB5oP0BRsWlGS08E0YSu8AZ9SofhkKGNab3IzsDC8OfKpl2KY8JO/DZFmeOefyIj6N/8VxDs3+s4UCsVnJBm2G1JGPE9wc2rRl2wp2v/k+/IBSID+lghHtqU42pvkie4ku9tjWKqc3yOP4zpM5acYz43fV5SnC9OUveWpFyEzRHOomeZQMzuSO3i241maQ820hFpoCjVVx6lgSkWTFY8c6it6vZm4JPvNKNUgUz5+5H+SlUn+06/Cb38OXvl1OPqzqjKIQvEIoesaO1pj7GiN8a2nZDR7sVjm7N05ProrJfv1utxs29TZ1xHnie4EB7uTPNGdoL8liqHSRrYEQgjmi/OM58aZyE0wmZ+sjidyE0zm5PZMYWbZsRoa6WBaynJYynJzqJmWsBTlllBLVaQjVmQDPp1CsTlQdarXmw9+B/70V+FXz0GyZ6Pv5v5MXZNifectaDsIL/wa7PtJ0I2NvjOFQrEOCCEYnMnx8dA854bm+HhonvPD8+RKLiDrZu/vSnCoK8GhbVK0e9JhVW1knSmUC1UpnsxPMpGbkONc47jklZYdmw6maQ230hpupSXUQlu4TY7DLVVZVlFlhaKRe9WpVlK93vyXvwun/zX83eGtEfkVAs79Ibzxj2H6GkTb4MA3YMfL0P2MemGMQvGY4XqCm5OLnB2a5+zQHGeH57kwskCpLEuVJUIWh7oTHOxKcKg7yaHuBB2JoBLtT0mhXGAsO8ZYboyx7Bij2VHGs+OMZceqkeaF0sKy40JmqCrLreFWWkOtjdu+RKuycArFJ0dJ9Wbh330DFifgb57c6Dv5ZHguXPkz+Pj35OvN3RJoOjTtgFSfjLoH4mBHwAoDQh7jlUG4ciy8FZqQ6+0IBKIQTECso9Ys9SILhWKz47geV8czvmhL2b4ylqHsyZ8vzdEA+zvjfkuwvzNOTzr82FcccTyHidyElOalzZfoueLcsuOagk20R9ppC7fREm6MLlfGUSuqfpFRKNYIJdWbhd88KCO83/y/NvpOPj3FRRh6HwZ/KB9mnL0D83ehmJECfT80vbEBlAv3Xh/rhJZd0LIHWnZD51GZj66iKwrFpqbguFwaXeDcsBTtCyMLXBuviXY0YLKvI86+Otne0RrFNrfAX/AeAk94TOenGc2OLhPl8ew4o9lRpvJTCBp/BsftOO2RdtnC7bWx39rCbdiGqsyiUGwk6jXlm4FSDubuwuHvbPSdfDYCURj4vGz1CCEj2E4O0OQLbnRD9ppx73QXz5XHFBchPwuZUdkWRmDmJkxehg//LVTql5pB6DgM3U9B73Hoe15GuBUKxaYhaBnV2tkVimWXa+OLXBiRkn1hZIHf/+BuNUfbNnR2tkUbItp7O+JENuHLalzPZTI/ycjiCCPZEdlXmr/teE7DMSEzRFu4jY5IB893Pb+iPKvScQrF1kVFqteTsXPwfz4P3/wdOPD1jb6brYXnwdwdGPkQhj6QbfRjcIsy4t15FPpfhO0vwrZjKm1EodgiuJ7g9nTWl+x5Lo4scH54ntmcFFJNg+1NEfb5gr2nPcaejjida5ynXfbKTOQmqpI8vDjM6OIoI4tyPJYbW1ZSrinYRFe0i45oB53RTjojnXREOqrCHLfjKiVDoXgEUOkfm4Hz/wH+8FX4m29D+4GNvputT7ko01BuvgG33pCiLVwZye57HgZelg9UNu9Sb4dUKLYQQghG5wtV0b4wssDFkQWG5/LVNbGgKQW7Pc7u9hh7O2LsaosRCz5capgnPCZyEwxlhhhaHKrK8sjiSDVlw12SztYaaq0Kc1e0i45IB13RLjqjUp6DpvplXqF4HFBSvRl4/Tdk+3ujYIU2+m4ePYoZuPMO3PgB3HgNpq7K+Xi3TFXZ8TL0vwSh1P3OolAoNikLBYerYxkuj2W4PLbA5dEMV8YyZIq1iHF3KsSedhnR7m+1SMQzeMYUo9lhhhaHGMoMcTdzl+HF4Yb0DA2NtkgbnZFOGWX2I82VcUekQ+UyKxQKQEn15uAPX5XR1F89u9F38ngwNwg3vg/XX5PR7OK8TBXperIWxe48ql7FrlBsUTzhMZmb5KPRG3w0coMr07e5mxlitjRGSZtAMxcb1puESNkddEW72ZnuZU9zH9ti2+iOdtMeaVfl5RQKxUOhpHoz8M+eh3gH/LU/2Og7efxwyzB8Wkawr78mc7OFJx9w7H+pJtmJ7o2+U4VCUUfZKzO6OMqdzB3uLNzhbuZuQ7S56Bara3VNpz3cTnesm45IFyGtlXIxxUImwchUiGtjHlOZ2gtQIrbBjrYYO1uj7GyNsqstxo7WKF3J0GNf7k+hUNwbVf1jo/E8mL4uH6ZTrD+GCT3HZPv8fw+5Gbj5ui/Z34eLfyzXNe+Wcj3wsqwsYqsn8RWKtcb1XEazowwuDHInc0f2C3cYzAwynBmmLGrpHWEzzLbYNrYntnOi+wTd0W66Y7J1RjofGG2ezZa4NrHItYkM18Zl/8bVSf7w9FDtGrbBjtYoO3zRltIdozulZFuhUNwbFaleL+buwm8egB//3+CpVzf6bhT1CCHL9l1/TUr2nXdk7WwjIMW6Itmte9UDjwrFp8QTHuPZ8UZp9iV6KDPUkN8cMkP0xHroiffQG++lJ+b38R6agk1rUkFjLlfi+sQiV33RluMM4wu1SHjQ0tnhC/bOtij9zVEGWiL0NkUemfraCoXiwaj0j43m1pvwf38FvvvHMt1AsXlx8nDnbRnBvvF9mLwk52MdMPAF6Pkc9Dwr3yapJFuhaGCuMMethVvcnr/Nrflb1Yjz3czdhlSNgBFgW2xbVZZ7Y71ViW4JtWya0nPzeYfrE4tcG89wzRft6xOLjM7XXlqla9CTDtPfEqW/OcJAq+z7W6I0R+1N81kUCsXqoNI/NpqZm7JPbd/Y+1A8GCsEO16RDWB+WMr1jdfkq9rP/D9yPtwka2JvOyYlu+Owqo+teCwoe2VGFke4NX+LW/O3uL1wuzqeLc5W11m6xbbYNnriPTzX+VxVmnvjvbSGW9G1zR/dTYQsnuxN8WRvY9WgTMHh1lSWm5NZbkwuVvu3r09RLHvVdbGgyUBLlP6WiOx96e5tChMwjfX+OAqFYg1RUr1ezNwC3VIPwm1FEl1w9GdkEwKmrsHdUzD4ruyv/Ge5zrCh8wh0Py0rjHQ9CckeFc1WbFkypQy35283SPOt+VsMZgYb0jXSwTR98T6+0PMFtie2yxbfTme0E0N/NMUxFrQ41J3kUHeyYd7zBMNzeW5OZblZJ9vvXJ/mjz4crq7TNehOhelvidDfHGV7c5jepgh9TRE6k0FMY/P/wqFQKBpR6R/rxf/7MzBxEf6b0xt9J4rVZnES7r5bE+3Kmx5BRrMrgt31pCzhF2na2PtVKOoQQjCZn+T63HVuzt1sEOjJ/GR1naEZ1QcE+xJ9bI9vrwp0IpDYwE+wdcgWy9yakpJ9Y7Im3bemsuSd2otmLENjWypMb1OYvmYp2r1NYbY3R+hKhpRwKxQbjEr/2Ghmb0G6f6PvQrEWRFtg74/LBlAuyV+ghk/D8Ieyv/aXgP8LbKpPynVFtDueUFVGFGuOEIKJ3AQ35m9wY66uzd8gU8pU18XsGP2Jfo53Hq9Kc1+ij23RbaqO82ckEjA50JXgQFfjLyFCCCYyRW5PZbk9neX2dI4701luT+V499YMuVJNuE1dozsVapDtyrg7FcJSwq1QbBhKqtcDIWDmNvQc3+g7UawHpg2dh2V7+uflXDEjI9jDp2Ubeh8u/JHcpxnQssc/5ojMzW4/oN66qfhUVOXZF+Z6gc44NXlOBpIMJAf4se0/Rn+inx3JHfQn+9esuobi3miaRls8SFs8yLH+xr9kCSGYXCxyZzrHramslG1fuj+4Pcti3dskDV2jKxmitylMdypMTzrMtnRI9qkwybCl/t8qFGuIkur1IDsFpYyKVD/OBGLQ97xsFRYn/Ej2BzByBq7+ee0hSM2QJfw6D0vJ7jwKbfvVg5CKKtW0jdnrVXmupHCsKM/9NXkeSA6QDqaVYG0BNE2jNRakNRbk6b50wz4hBNPZEnems9yayvl9lruzef78whgz2VLD+ljApDsdpicdYlsqTE+TlO1t6TDdqRBB69HMf1co1gsl1evB7C3Zp1XlD0Ud0VbY/SXZQP5FY2EYRj6Skj16RlYb+ejfyf26KUW7w49odx6GtgNgBjbuMyjWhZyT48bcDa7OXuXa3DWuzl7l6uxV5ovz1TX18jyQHGAgMcBAcoCmkMrhf1TRNI3maIDmaIAne9PL9i8Wy9ydyXF3JsfgTI6h2TyDMzluTmZ5/cpkQ5USgLZ4QMp2OuzLd5htqRDd6TBtsYDK5VYoHsC6S7WmaV8CfgswgH8phPiNJfv/W+BvAGVgEnhVCHFnve9zVVHl9BQPg6bJ6jCJbtj7FTknBMwPSdEePSP7y/8ffPRv5X7dhNZ9jakjbfuVaG9RXM9laHGIa7M1cb42e427mbsIPyc/ZIbYmdzJKz2vsDO1k53JnUqeFSsSDZjs7YiztyO+bF8lrURKt5Ttiny/e2uG/3hmmPo6Boau0R4P0pUM0ZUKVfvOpD9OhgjZKtKteLxZV6nWNM0A/g/gi8AQ8L6maX8ihLhYt+wj4CkhRE7TtL8F/C/At9fzPledmVuABqnejb4TxVZD0yC5TbZ9X5VzQsDcYE2yR87AxT+BD/+N3K9b0LavJtmdR6R4m/bGfQ7FMmYLs1V5vjZ3jaszV7kxf4N8OQ+AhkZvvJfd6d38+MCPsyu5i12pXXTFurZEfWfF5qY+reTJFX40lcoeI3P5aoR7ZC7P8Fye4dk8792aYWyhgOs1Vg9rithStBON4l2RbpXTrXjUWe9I9TPAdSHETQBN0/498BNAVaqFED+oW38K+M663uFaMHNTRh9V9FCxGmj+L2ipXtj3E3JOCJi705g6cuE/wul/Lfcbth/RPlKLarfsVaK9Driey2BmkMszl7k8c5krM1e4Onu1oVxdKpBiV2oX39j5DXalpDz3J/sJmephVcXGYJu6rCrSHFlxf9n1GM8UGZ7NMzyXY2SuwNCsFO9rExlevzpBwWlMLwnbBl1JP7qdCtERD9KeCNKZDNGeCNKRCBK2VVaqYuuy3l+9XcDduu0h4Nh91v888GdrekfrwewtlU+tWFs0TZbqS/XB/q/JOSFg9nZj6sj5P4LTvyP3G7bM0W4/5LeDsupIILZBH2LrU3SLXJ+9zqWZS1WJvjp7tRp9NnWTHckdfK7zc+xK7WJncie70rtUxQ3FlsM09GoEGpbncwshmM05VekenivUjfOcG55f9iAlQDxo0pEI0ZGUkt0eD8nel+6OZIhoQIm3YnOy3l+ZK/3UWPHtM5qmfQd4CnjxHvt/EfhFgJ6entW6v7Vh5ibs+fGNvgvF44amyV/m0tvhwNflnBDy67Ei2WPnGnO0QVapaT/otydkH2tXb4ZcwnxxniszV6ryfGnmErfmb+EKWVM4YkXYndrN13d+nd2p3ext2stAYkDVelY8FmiaRjpik47YHOxe+eVABcdlfKHA6HyBsflKn2fE3z4/vMDUYnHZcbGASXudaLcnQnT62+2JIG2xoEo1UWwI6y3VQ8C2uu1uYGTpIk3TXgH+HvCiEGL5vyhACPEvgH8B8o2Kq3+rq0RhHnLTqpyeYnOgadA0INuBb8g5ISAzKgV79CyMnZX9xT+uHRdulnLdURfVbtoBj+grqOsRQjCeG+fS9CUuz17m8rSU6JFs7VtXS6iFPek9fH7b59mT3sPe9F6V+6xQPICgZdDbFKG3aeUUE5C53RXxHp3P18m33L4ylmFyscjSl0Pbhk5LLEBbPFCtAS63g7TFA7TGZJ8IKflWrB7rLdXvAzs1TdsODAM/Bfx0/QJN044A/xz4khBiYp3vb/WZUeX0FJscTYN4p2y7frQ2X5iH8QtStiui/cPfBs+R+82QrDTStg9a6/ot/Br2yotTLkxf4OL0xWo/U5gBag8PHmo5xLd2f4s96T3sTu+mOdS8wXeuUDya2KbOtrSspX0vHNdjIlNkbD7P6HyBiYUi4xnZT2QKXJtY5K3rU2QK5WXH2qZO6xLZbo0HaItJEa+M4yFTyfc6I4RAlEqIYrHae8USouRvOw7hJ5/c6NtsYF2lWghR1jTtvwb+HFlS718JIS5omvb3gQ+EEH8C/K9AFPgD/wt4UAjx1fW8z1WlWqNaRaoVW4xgAnqPy1ahXIKpqzXRHjsHl/60VnkEINomH4ps2+/3+6B596Z8FftkbrIqzxWBnspPAaBrOgPJAV7oeoF9TfvY17SPXaldhK3N9zkUiscZqyG/+97kSy4TmQLjC0XGFwpMZIpMLBSq4ytjGU5enSJTXC7fAVOnNS5rgrdEAzTH/HEsQEvUpsXfbo4GiDxCOd9CCCm1hQJesSjFtlComyshigU5VygiSkW8QrE2V/RluFSU46okF/FKpep+USziOY3bwnHuf3O6zp4L5zfVLzvr/n9eCPGfgf+8ZO5/rBu/st73tKZUa1T3behtKBSrgmnLhxnbDwB/Vc4JAYvjMqo9cRHGL8LEBXj/X0K5INdouqzTvjSqnd6+bikk0/npxgj01EUm8vKPYRoa/Yl+jnceZ1/TPvY37Wd3ereqvqFQPEKE7AenmwDkSmUZ7fZlu17ApxZL3JnOcfrOLDO50rK0E5BVTqRgN8p2S1XEbVqiQZpj9ieudiIcBy+fx8sXEIW8L7OFmsgWi1Jui5W5Il6xUJvz99fmiv5cQc4VSzWBLhQQpeUPkz40moYWDKLbNlog4DcbzbbRbbmtJ8Nogdq2ZttyOxBAs5du23Kubnuz8ej8OrVZmRuU+aiqooLiUUXT5IOMsXbY8XJt3nPlL5UV2a4I96U/pfp8shmClt0yot26B1r2QPMuSPaC/unzkRdKC5yfPM/56fNcmLrAxZmLjGXH5O2i0Zfo45mOZ6oCvSe9R0WgFQoFAGHbpK/ZvGc5wQpl12MmW2JyscjkQoHp+Ryz0wvMzi6QmcuQmZ0keyfLYCbL9WyOoFsi4DoE3BLBshxHKZPQXeK4RHEIe2WCnlxjl0uYpSJGqYhWlFJMeXkU/aEwTSmiwaDsl4z15iasQBAtGPDnguhB2WuBQHUse/+YYHDJOIgesKvnxXr88tWVVK81c4OQ3OTVSRSKtUA3oHmnbPt/sjZfysHk5cao9o3X4OPfra0xQ/K4lj1Suit9ajsYjd+2HNfh6txVzk2e49zUOc5OnuX2wu3q/r54H0daj7C/aT/7m/azt2kvEev+PywVCsWjiXAcvFxOtnweL+uPc1lEPl/bl8vh5ZZs53OIvJ/WkM/h+WMzn6etUKDNdT/x/ZStAI5lUzRsCoZFTreY00wKhk3RiFAwUxSDNkXDomjYEAhgRMJY4TCBaJhgJEw4FiYSjxKLh4kloiQSUVKpCKlUjGAkLMXXVLq3Hqj/ymvN3CC0Hdjou1AoNg92GLqOylZPfhYmr0rhnrwi+8Efwrnfry4Rhs1wcz/nkm2cDQQ452W5lB+j5D88mQ6mOdR8iK8MfIWDzQfZ37yfuL38Fc0KhWJzIzxPSm02i5fL4uVyjdKb9aXYF+Lq/myuUZrrpFjkcg/O063HNNHD4VoLBtHCIYx4HL2tDS0URA+G0ENBtFCoNg6G0MMhGbFdMqcHK2uDaMHgipFc1xPM5UrMZEtMZ+v6xRIz2SIT2RLTi7X52akS7oQASsCM3yTRgFktbdjk9+moTSpskwpbJMON42TYwjJU1aJPi5LqtcTzYO4u7P6xjb4ThWLzE0pBzzHZfBZKC5wfeY+zd9/k3ORZzmfvMuPloHSLQMFjX6nETxVLHCyWORRqp8PuQqMFvBh4FrjefS6oUChWEynCOSnC2Sze4iJeNovr995idvm+7JJ9lbW5HCsmLK+ErkvpDYXQw2G0iJRgI5nE6uysE+NQdayFw+ihOmGO1I6vrtmgnF1D12iKBmiKBtj5EOs9T7BQcGoC7gv3TLbIdN32yHyB8yPypTuOe+//trGASTJikQrbvnRXxo19dRyxidjGY5fqsRJKqteS7AS4RZX+oVA8BK7ncn3uOmcmznB26uyyNI7+RD8vbP8yh1oOcbD5IDui3Vgzt2RUe+pKLcJ99b+AqPszbKRF1tRu2iFTSpr8lJRUH6gXsSgUiHIZb3FRym8mg5vJ1PrFOtHNVkR4BQleXJQi/DCYJkYkgl5p0ShGIoHV1SXlNhLBiEZr+yORRmkOh9HDkaoka4HAYy10uq75UWabgZYHrxdCkCu5zOZKzOUcZnMlZnMOc7kSs1nHn6/N3Z7KMpsrrViSsIJlaFUBrxfxRNgiEbJIhmwSIWtZiwVNdP3R+X+npHotmRuUfbJ3Y+9DodiEZEoZzk6e5czkGSk9KUzNAAAgAElEQVTSk2fJleUP5aZgEwdbDlbTOA40HyBmr/Cwb8ch2epxHfl69qlrMH3N769L2a5/c6RuSrFu2gnNvnRXhDvSot4gqdgSCNeVUtsgw4t4i5XtRdzMAl51zhfnxcq+DOJhZNiyaiLsC6+RTGJ1d8lxJNqwT44j8piGuais4qD+fW0YmqYRCZhEAibdqYc/znE95vNOVbhnsytIuT++NZXlw9wc8zmH0n3+YqhpEA8ul+2KjN+zhS1igc1XO1xJ9VpSlWoVqVY83gghuJu5y0cTH1Ul+sbcDQQCXdPZldrFVwa+wuHWwxxuOUxXtOvTf7M0rNoDkkvJz8L0jeXCfeP78q9KFQIJX7R3yrdPpvv9V773yzQVhWKVEEJIKZ6fx11YwJ1fwF2Yx6uOK9s1EfYyC1U59rLZB15Ds230WAwjFvP7KGZrK3osihGNocf9fdGYnPPHRjwmhTgaRd+E5csU64tl6NXygA+LEIKCI2W8IuSV8XzeYaFuPOf3I/P56vz90lRMXePKP/gyxiaKdCupXkvm7sg+ue3+6xSKR4xCucDF6YtVgf548uPqWwljVoxDrYf40b4f5XDrYQ42H1y/ahyhFHQ/JVs9ngvzd2HqupTt6etSuG+fhLP/fvk50v2Qrsh2XQunVYT7MeT+Yjx/b1GeX8DNZOB+VSMMQz4YF49JAY7FsPv66qR3iQjHouixuN/L9UqIFRuFpmmEbIOQbdCeCH6iY4UQ5B2XuZzTIOIVGc+V3E0l1KCkem2p1Ki2VfkuxaPNVH6KD8c/5MzkGT6e+JiLMxcpezL/ri/exwtdL1Sj0P3JfnRtkz1drhsyFSTVBzuXvH/Kyct0kpmbtTZ9AwZPwbk/oFpzG2SEuxLRXtqirUq4NzlCCJkaMTd3nzYvRflTiLERj6MnEhiJBPa2beiJOEY8Ifcl/H3xBEbCXxtPoEfCm+5P3ArFeqBpGmHbJGybdD7gbZmbBSXVa4mqUa14BBFCMLw4zOnx03w48SGnx09zZ0H+VSZgBNjftJ/v7vsuh1sO80TrE6SD6Q2+48+IFYLWvbItpVyE2TuNwj1zE0Y+got/3PjApBWRcp3qlfKe9PtUr/w+YW2NHxpbBVEqSfn1Zbh8L0FeMndPOdY0KbrJBEYiqcRYoVAsQ0n1WqJqVCseATzhcWPuBh+OS4E+PXGaiZx8vXfcjnO09Sjf2PkNjrYdZV96H9bjVFHDDEDLLtmW4jrye8DMrTrh9vO5r3+v9gr3CtG2JaLdW+vjXcteevM4ITxPCvLsLO7MDOWZGdyZWdzZGcrTM3J+iRzfL9dYs22MZLLaAgMDDdtGKoWRTDTOxeNohrGOn1qhUGw1Ht/v0muNqlGt2KI4nsOl6UtVif5o8iPmi/MAtIZaebLtSY62HeVo21F2JHdsvlSOzYJhyYccmwaW7xMCFsdllHvujt/flv3gKTj/hyDqnpjXTUh010S7PtKd7IVI85ZKLRGuKyW5Ksh1ojwzQ3m2fjyLOzt7zwiyHo1KCU6lMJrS2AP9DTJs1oux37RQSEWOFQrFqqOkeq1QNaoVW4R8Oc/ZybNSoidOc3byLPlyHoDeeC9f2PaFqkh3R7uVjKwGmgaxdtnqXnZTxXVgfsgX7tuN8n3lzyA72bjeDEnpTnTLB6MTleZvx7vWtCZ35UE9d2qK8vQ05ckpytNTuNNLBNkXaHd+XgYeVkBPJDBTKYx0Gqu3h9DhwxjpNGZTGiOVxkinMNNpjHQaI5VSD+EpFIpNg5LqtULVqFZsUgrlAh9Pfsz7Y+/z/tj7nJ06S9kro6GxO72br+34GkfbjvJk25M0h5o3+nYfTwzLf+Bx+8r7i4vye0xFtOfvyjZ3F65ckL/UN6BBrMMX7u464e6pbQcbX+cuRTmHOz1FeWqK8tS0FOXqeJry1CSuPxaFJeksIPOQk0kpxamUTLN4+ikpxQ2C3ISZTskosvUYpQ8pFIpHCiXVa4WqUa3YJBTdImcnz1Yl+uPJj3E8B13T2Zfex8/s/Rmean+Kw62HidvxB59QsfEEotC2T7aVcAqwMCy/D80P1YR7/i7e7Q8oj/8p5ZygXNApF3TcgkHZCVIuh3GLFuW8oLxYQpRWSLnQNCnJzc2YTU3Yvb2YzS2YTU2YzU0Yzc3VfUYqpfKQFQrFY4OS6rVC1ahWbBAlt8S5qXO8N/YeH4x9wJmJM5S8Ehoae5v28tN7fppnOp7hSOuRld9SqNiSePk85clJyhMTDb1T3ZZzXsYBmhoP1sCI2JhhHTNQIpQsYLYUMIMuZtDDCHpynE5gtHSgJbsg3um3rsZelRBVKBSPKUqq1wpVo1qxTjiuw/np87w3+h7vj7/PxxMfU3ALaGjsSe/h23u+zTPtz3C07aiKRG9BVpLlBlGerMhyZtmxmmVhtrZitrQQGBgg8rnPYba0yLnmZszmJszmZhlRNpf8OChmYGFURrwXRvzmj+eH4e57kJ9ZfsPBRJ1od648DsS31IOVCoVC8TAoqV4rVI1qxRrhei6XZy9zauQU746+y5nJM9UHC3eldvHNXd/k6fanebLtSRKBxAbfreJeCCFk/eTxcZyxMcpj4zjjsi+Pj+GMT3w6WW5pwWxtwWptRU8kPv2DpYEYtMRWLhdYwcnXCffIcgEfPbtCfjdghWUJwVgHxPx+pe1gQsm3QqHYMiipXitUjWrFKiGE4G7mLqdGT3Fq9BTvjb1XLXG3I7mDr+34Gk+3P81TbU+RDCY3+G4V4NdVnpnBqQjyEmmu9KJYbDxQ1zFbW7Ha2gj096+NLK8mVujeZQMrlEuQGW2U7sVxOZcZl+J99S/AWaGutBm6v3RXtoNJJd8KhWLDUVK9Fqga1YrPyHR+mndH3+XdsXc5NXKKkewIAO2Rdj6/7fM82/EsxzqOqeocG4AQAnd6GmdkBGd0zJfmccpjYzjjfj8xAY7TeKBlYbW2Yra3E9p/APPlV7Da2zDb2mXf3o7Z1LQ8DWOrY9p+be0HVEIqZqRkZ0brpHtMtsVxGD8P11+D0vLIPWawUbIjrfK18JEWv/e3o63qzZUKhWLNeMS+e28SVI1qxSck5+Q4PX66Go2+OnsVgJgd41j7MX7uwM/xbMez9MZ7N0eE8hHGK5Uoj47ijI7ijIz68jyCMzJCeUTOi1Kp4RgtEMBsb8Nqayf05FHibe1yu729Ks1GOo2mqxfl3JNATLbmHfdfV1z0pXtsiYD7/cQlWHwDCnMrH2/HINrii3alb6sb18m4eiZGoVB8ApRUrwWqRrXiATiew4WpC/xw9IecGjlVrRVt6RZHW4/yK0d/hWc7nmVvei+GrkqSrRZCCLyFBV+UR3GG/b5OnN3JqcaDNA2zpQWro4Pg/n1EX3kZq7MTq6MTq6Mds71d1ldWv+ysD4GobPdLOQGZdpKdlEGOxUkp35VxdgIWJ+Qr42+/vfIDlwBWpBbhro96R5oh3OT3zbIPpR/rV8krFAol1WuDqlGtWIGhzBDvjLzD28Nv8+7Yu2SdbLXM3Xf3fZdnO57lSOsRgmZwo291yyKEwJufpzQ0jDM0hDM8RGloCGd4WEafh0fwcrmGY7RAAKujA6uzg8CLL/rjLtl3dWK2tam39m1FTBsSXbI9CNeRAr44UdfXC/g4TN+AwR9CbgYQK58nlKpJdrhpuXgv3TYDq/qRFQrFxqKkei1QNaoVyJSO98fe5+2Rt3ln5B3uLMivi45IB1/q+xLHO4/zTPsz6uHCT4iXz+MM+bLsy3NpuDb2Fhcb1uuJBFZXJ1ZvL+FnP+dHmaUwWx0dGE1NKsr8uGNYtbJ/D8Ity8h2dgpyU34/vXx75qYsO5ibBrHCS3RApqJEfPleJt5NMvodTtf6YFJFwxWKTYz617kWqBrVjyVCCK7OXuXtkbd5e/htPpz4kLJXJmgEear9KX5q909xvOs42+PblcTdB+E4OGNjy8RZyvMw7lRjeoYWDGJ1d2F3dRN+8kms7m653d2N1d2NEVMvuFGsIoZZSwl5GDxP5ncvE+8pyE7XtjMjMHZObrule58vkIBwarlwh1KN4/q5QExVR1Eo1gEl1WuBqlH92DBTmOGHIz/knZF3eGfkHabyUvh2pnbynb3f4XjncY62HSVgqD/z1uPl85Tu3sUZHKR0Z5DS4CDOXTl2RkeliFQwDBlZ7u4m+tKLUpa7auJsNDerX1IUmxddl4IbTkPzzgevFwJKi1K087MyKp6r9DN1czNS1KeuQX4O/DKbK9+DVSfaFeleIuahpIyEBxO1cSAu71+hUDwUSqrXAlWj+pHF8Rw+nvhY5kaPvM2l6UsIBMlAks91fI7jXcc53nmc1vBDRrEeYdxMRspyRZzvDuL4Al2eaHwhiJFIYPX2Ejp8mPhXv1Inzt1Y7W2PXpk5heJeaFqtEgrbH/4415FyXZVvX8Ar4+rcHMzehpEP5ZxbvM9JNSnZ9aK9knxX55bsV6kqiscM9RW/2qga1Y8c49lx3hp+i5PDJzk1eoqsk8XQDJ5oeYJfPvzLPNf13GNZpaPyRkDnzh1Kg4OUBu9SGrxTFWd3drZhvdHSjN3TS+S557B7e7C2bcPu6cXu2YaRUG9+VCg+E4YlywJGWx7+GCHAyUm5LszLNJX8XF2/wlxmVM7n5x4g5Mic8fsJeSAuf3kIxuW42idkb6oHhBVbCyXVq42qUb3lKXtlzk6e5eTwSU4OneTK7BVAvnjly9u/zHOdz3Gs4xgx+/HI1fXyeSnNt27Jdvs2xVu3Kd2+jbewUFuoaZgd7dg9vcS++EXsnm1YPT3Yvb3Y3d3oEfWMgUKxqdA0+eyPHQE+xYP1Tv7BEl4/N3Ozts/JPfj8ZnCJbNf3Cb+P3WdfHCxVTUmxfiipXm1UOb0tyUxhhreH3+bk0EneHnmbhdIChmZwpPUIv/bkr3Gi6wQDyYFHNndXuC7O6FiDOJdu36J4+zblkdGGtWZ7O/b2PuJ/5cekMPvN6upCD6jccYXiscEKyRbv+OTHug4UFmQueGFBvlGzuOCPF5bsq5vPjNXGpcUHX8ewl0u3HfPrncfA9uueV+YatuvnYvKvAQrFfVBSvdqoF79sCTzhcWn6Em8Ov8nJoZOcnzqPQNAUbOLz2z7Pie4TPNv5LHE7vtG3uqq4c3MUb92i5EeaqwJ9507DWwL1aBR7+3bCTz6F/c0+An192Nu3Y/f2oofDG/gJFArFI4FhyXKCkaZPfw7PXUHE6/p77cvd8SU+I8X8ftVWGu450CjZDVK+RNIDsXuIur9thdVDoI8gSqpXG1WjetOyUFrgnZF3ODl0kreG32KmMIOGxsHmg/zS4V/ihe4X2Jvei65t7W90QgjKExMUr1+ndOMmxRs3KN24QfHGjcY8Z9PE7u7G3r6dyPPPY2/vI7B9O3Zfn6qooVAoNj+64ZcNTH2285RLUq4rkl3MQHERSpV+sW67fi4jSyDO3q4d+zDR8wpWWLZKCo4d8bejYPvzVmVfuCbjD1r/gAdEhRDy/UWeQHgC/Ca85fPC30YIhFcbI/DXL11H7ZwC/7jKOv/a3pL56jH18/XXrT9X3T0Aya884M2q64yS6tVG1ajeNAghuD53nTeH3uTk8EnOTJzBFS5xO85znc/xQvcLPNf1HOlgeqNv9VMhPA9neFjK882bFK/foHjzBqUbNxtegKLH4wQGBoi98jJ233YZcd7eh93djWapP2cqFIpHlwaBdH0BdD0peJ4HbkUgAwjXBi+NQIApELoAq04wXVETPbdO+HzRk2MPnCLCKYJTqvaUSwjHkQLvlhHlst+7UHah6CFcVx5fvUch71EA6AhRBhYR5IEZwECgA3ptLAzQDASGP2cs2a/521sMHfkMgKah+WPN0JRUP/KoGtUbiuM6nJ44zet3X+f1u68zvDgMwJ70Hl498CovdL/AweaDmPrW+dIXjkNpcLAu4uxHn2/dQhQK1XVGSzOB/gESX/0q9kA/gYEdBAb6VdRZoVA8NDWB9IXTXToW4HoNfeNc3TEVEa2Iq+vVzu/VzTcI75J+6X7/PMvn7rX2Hq+UX080DfQgmh7yx74Y6pWx39saaDTMoWvyvT2aQMMDXDQ8NFygDMJFowyijCYcEGUQBTTPAa+EJkrgyaa5RRBFcItobgHcgjy27rzgAp4ca5W5WpPzGpi2LHVqWv5Y9pg2WDaaGQDLBivgjwNgB9GsgJ+LH0Czg2CH5MOkdrhuO4QWCIFh+BK9dX5+bR2z2CqoGtXrznxxnpPDJ3nj7hu8NfwWi84iASPAsY5j/PzBn+dE1wnaIm0bfZsPRLguztAQhatXKV67RvHqNYrXrlG6cwfK5eo6q7MTe2CAyLFjjfKsytIpFJsSIepkr+whygJR9mqyWvb85sto2ZfVsgf+XHVfvbCWG8cVGa7J7cpivJIMSxGVEdw1x6gTSaNOLI2lvd4onZaOtnRt/TmWnUsHneq5VrzG0uNWOJ8c6w0y3Ci9Wu069aJcmd+sQQ0h5AOjTk5Wcqn05cLyuWp/r7nZ2lx2hXWfBt2SAm4GpXiboeX9X/29TfW2UCXVq4mqUb1u3Fm4U41GfzTxEa5wSQfT/Ejfj/Bi94s82/EsYWtzPlAnhKA8OdkgzsWrVylev94Qeba2bSOwcyexl18mMNCPPbCDwPY+VZpOoXgIhBBSSCvC6izp/TFlr1Fqy54UzTqZxRfgBumt7q8X4+VSLMp+ZHW1A6aGL32GjnafcUVG9aAhx6ZeFUbN0O97nsq+qlCa9ePaXEU6G8aG1iDHDeKq2Bz4EWdMW9YNXyuE8EU9fx8xX0nsV+5FKY8o5hD5DMYmEmpQUr26qBrVa4bruXw8+TGvD0mRvjV/C5CvA3/1wKu8tO0lDjQf2HQPGbqLi1Kcq9Fn2btzc9U1RnMzwV07SX37WwR27SKwcyeBgQElz4pHAuEJKbKOiyj5vbNEZP1tlgjvMgmuF+F77hd+nuoqWKyGFEJTSqRmaGDqVYHUTF9KAwZ62JJSWb/f0OW2WSedhi7PVX983dz9jqcquJs4+rmJEH7Os/AfhKv18oE3IQSe/xCc589XxvVzlbX3PNcK5733df3tFdYuv+6SczzE52lYW3m4r+56te0l+0Qt/7zxMzWuW3E/Sz7PCufmnvtNhIghRNQ/d90ab+XrVtA0+KX1/ZJ6IEqqVxNVTm9VyZfzvDP8Dt+/+31ODp1ktjiLqZs83fY03979bV7a9hJd0a6Nvk1Apm6Ubt+mcPkyxcuXKV69RuHa1YYaz3o4LCPPX/yiFOdduwjs2omZ3poPSiq2NjKSWhHdOtmtF1/Hw3OWrCn58lqqrREl15+Ta7y683ymnFYN+Sd/U6/21I21gIEesXwhrVtT2V+/1tTRLF+OLaMmsJU1y8S27k/7m4SKVHhlD8/PIfZcKYaeK5bMVdb48ljZ5z9k51WEpTr214jaOSriVJn3/Dxl4Qk8z9/XMOdfb8X5Jcc0XEce13D9B16n8XorieWjiKbJNBPNf2BP83OOa/ONc1S26+YbzyM3tLp1Ddt1v8DphtZwrtq6umMq56Tu/urPrWv4y6v/vmrno2Ft5fpQO/fSz7PZUFK9mqgXv3xm5ovzvDn0Jq8Nvsbbw29TcAvE7Tgnuk/w0raXeK7zOaJ2dEPv0V3MUrx6RQr0pcsUrlyhePVqLXXDsghs3074yFEC35biHNi5C6urc1N+E1BsXoQQNWktyd4ruv62nPMq46Ivs3X7Pf8YUZQC7BXdqhx/KtmtSK5lyN6uGwcM9Kgt50wd3fbnLR2tfmwZjbLrz1cF19Rqa4xP9+/F80RVPF3X7/1tryyF0y0LPEfg5Z0V11WkrV5WXf9Bu8qc5+dJV8XWE3h+jnL12IZzeCucc6kcLz++/hqbDd1P6dAMDd0Xn6p86Zq/n7qx1jDW6/aZtt64TvNFzpevyrh6nbrzLRPLemFbMqf7cqYvXVsvgXrtM6x43qVC+xBr669bkcPGe7mPKG+yX/AUK6OkejVRNao/FVP5Kb4/+H1eG3yN90bfoyzKtIZb+drOr/FKzyscbTu6IdU6hBCUx8aq0efCpcsUrlzGuTNYXWMkEgT27CH17W8T2LuH4J49BPr70Wx73e9XsfGIsi+uRV9+i+XqtijUzVVEt16KS54vxrV9wnE/WS6uqaMHfHENGGi2gW7r6MmAPzZ8Eb6HGFfm6+b0Oul1/WimW5byWWleZdvxcF0prK5Tv9/Dzbl4brkqr0ult7YtxdItV+RziRQv2a6s9/z17lrkL98D3fDFztCqY13X0P0cYt0XzOq6um3T0uW6JWsqx2iGXjt+6TUMDV3Xa5K5ZJ+mL7nmCjKr6SzbXxXgOoFtHFMntio/WqFYipLq1UTVqH5ohjJDvDb4Gq8NvsaZiTMIBD2xHr67/7u83PPyuudHC8eheONGLfrsi7Q7P19dY/X2ENy9h+RP/iSBPVKgzfZ2FT3Y4ghX4BXKy0W4UJFjf1/Bj/42rG085mHzeCuR3Yr0arY/jlhYdduarSP8vFtP1xCGjqeBp2u4aLiawEUGncuCZbIrxdYXV8fDzZVxF5asKUuhrd+uCnFFbh1v1aOkFfEzDCmhulnZlrKom3ptn6FhB43qWDd0DH+9buoYuux1Q8Mw9apk1saN+2rX8M91j3tYKqyaLvdpxub987NCodg4lFSvJqpG9T2pvIilItKXZy4Dsn70Lx3+JV7ueZkdyR3r8kNKlEoUrl2jcOEChQsXKVy4QPHKFVmYH9ACAQK7dxP7kR/xo897CezahRFVvyxtNqrpEYUyXsHFy5el9BbKeHm3biz3r7ROlB6uhlhFhLENsGTerggYiLCF8KXXMzRcTcPToAy4moYjoCwE8vk6j5IncB1B2ZfecsnDzTmUSwXcskfZ8ef9/rOi6xq6JSXUMPUlzRdNU8cKmnLb8vdVJNRavr5+W6+MrdoxRt0xeuUYX1rrhVWhUCgeJZRUryZzg9B+cKPvYtPgCY/zU+erIn1n4Q4aGodbD/O3n/rbfKHnC2yLrW2qjFcqUbxy1Rdov127Br5A67EYwX37SP3MzxDct4/gvr3Yvb1ohrGm96WoITxRE99cpXcatwtlRF5Gg5eKMw+IoAoNsAyEpeMZGp6h4+oabsDEDZiUAUeAIwSOKyi5gqLrUXIERcel6AiKJRfH/5r5NBiWjmnpdb2B6Y9NWycQMev2G7I3dQzbX2/qmLbh9/62VRkbDeevSa0fVVXyqlAoFOuCkurVolKjes9f2eg72VDKXpkPxz/ke4Pf47XB15jITWBqJs90PMN3932Xz2/7PC3hljW5tlcsUrxyhcKFC+T9KHTx2rXqi1P0RILgvr00/ex3Ce7fT3D/fqxt29SfcFcJUfak8FakOFcvynWSnHNws7X9FN37ntfTNSnBfvTXARwPHE9QdAXFskexLGQ0WNQEueyP5dmXC7FuaJi2gWnrWLZRHZthE8vWCdsGcVv35w2sunHtGH/O8qV3iTybloFuqgeMFAqF4nFASfVq8RjXqC65JU6NnuJ7d77HD+7+gLniHEEjyPHO47xy9BVOdJ8gEVjdt/2Jcpni9evkz56lcO4c+bPnKF6/Dq5UKCOZJLh/P9Gf+zkp0Af2Y3V1Kbl5SIQnpBhnHbxsmfJiCWe+iDNfpJxx8BYdvJyD8KVYK7lo96kmIajJbskTlASUKtvCl2SxfN4zdMyAgRXQsYIGVmB5CwcMEgEDK2BK2Q3UCbJtNMqvL8OGLdMRFAqFQqFYLZRUrxaPWY3qnJPjreG3+N7g93hz6E2yTpaoFeXFbS/ycs/LPNf53Kq90VAIgTM8QuHcWfIfnyV/7hyFCxeqJeyMRILgwYNEX3qJ4P59hPbvx+xU5esquGWPwnyRwlSe0lyR0nwRd6GEuyijx9SJseF4GK6HIeR7L1ZCijGUhKDoS3DJEziAZ2gIy0DYBlrQgKCJHjQwQiZW0KwTY5PQUkFeIs1mwFDiq1AoFIotg5Lq1eIxqFFdqSH9l3f+kndG3qHoFkkFUnyp70u83PMyxzqOYRufvZScOzdH/tw5GYU+e478uXO4MzMAaLYtc6C//S2CBw8ROnTwkU/hEJ6gVHQpZh2K+TLFXJlS1qG4WMKZqwmyyDlohTJa0cNwXExXYAlBQAOz7r+P4TcAzxdjByjrGq6h49kmnq1DwICQiR4y0SMWRtTGjNnYEYtwyCQRMrCDpmwhGRFW+bsKhUKheFxRUr1aVGpUJx6tGtX3qiH9jZ3f4JXeVzjSeuQz1ZD2ikUKFy9WUzjy587W6kBrGoEdA0RfeonQoYMEDx4kuGsXmmWt0qdbf8qOS2GxTCHryLbY2BczJcqZEmKxBPkyelFGjwOaRkCHgEZ1HFvhFwkBlDVwTR0vZCICBsWQSSliYUQtKcWpIFYyQDAVxE7YWAHjkf6lRKFQKBSK9UBJ9WoxNwiRFrBXJ+VhoxBCcHP+Jm8MvcEbd9/go4mPGmpIv9LzCvub93+qGtJCCJyhIfJnzpD/6Az5jz+mcOVK9UFCs72d0MGDJL/5TUIHDxE8sB8jurFvT7wf5ZJLftEhnymRX/TFuCLJ2eWyLPJlzLIgqENQ0xr6kK6R1sFeKreGhjAMhK0jgiZayESPWhgxGzMewE4HsZMBjLiNEbXlK5s/5VvoFAqFQqFQfHqUVK8WW7hGddEt8sHYB7wx9AZvDr3J8OIwALtTu/lbT/wtXu59mZ3JnZ84mukVCrISx0cfkTtzhvyZj3GnpgDQw2GChw7R9OqrfhT6EFZb66p/tk9C2XHJZ6QI5zIlCpkSuYxDYbFEPlOT53xGbjt+1QoTCPliHNIhqGtEbJ2koRPUwRZgItBCS8r0aUDYwojbmIkAZjKAEbOlIMdt9JiNEfNFWaVVKBQKhUKxqVFSvVpssRrVE7kJTg6d5I2hNzg1eop8OU/QCHKs4xivHniVEyRvdxkAABuUSURBVN0naI+0P/T5hBCUR0fJnzkjBfqjMxQuX67Wg7Z6e4g+d5zQkSOEDh8msHPnmteCFkJQyDrk5kvkFmSrCHG+XpR9WXYKy0u76UDE1EhETOIhkxZTJxQxCYQNrLKHWfLQykte0KFRjSYb8UBNkOOV5s8pWVYoFAqF4pFBSfVqsAVqVHvC4+L0xWo0+uL0RQDaI+18deCrnOg+wTPtzxA0gw91PuE4FC5dInf6Q5nOceYM5fFxALRgkNDBgzT99b9O6MhhQk88gdnUtGqfxXU8svNFKcrzpdp4oUSufrxQwluhzJtuaISiFsGoRTxi0tYeIWJqhDSwPYHleOjFMmQdqBftgl/vOmphJAIYlehyIoCRtP1eRps1VbVCoVAoFIrHCiXVq8EmrVGddbL8cOSHvDH0BieHTjJdmEbXdA41H+JXjv4KJ7pPPHRah1cokD97ltwHH5D/4ANyZz5G5HIAWF1dhJ96qhqFDu7+bA8Tuq7H4kyBhekCmekCC1N5vy+Qmc6TnS8tP0iDUMwmkrAJx23SnRHCcZtI0CRsQEggZTnvIDIO7myB8mwRso3n0kImZiKA0RLG2GFLSa4X6HgAzVLCrFAoFAqFohEl1avB7G3Zb4Ia1UOZoepDhu+Pv0/ZKxOzYjzX9Rwnuk/wfNfzpIKpB57HXVyUudDvf0Dugw8onDuHcBxZkWPXLpJf+xrhp58idPQoVusny4X2XI/FuWKDKNcLdHauiKgLMGsaRFNB4s1Btu1LE28OEUkGiCQChEIGAVdg5h28+RLlmYIU5uk87vVZhCNTMwRQAvSwiZEKYrWFCe5JY6aDGKkgZiqAkQyiB9TryRUKhUKhUHxylFSvBjO3ZJ/uX/dLe8Lj/NR5Xr/7Oj+4+wOuz10HYHtiO9/Z+x1OdJ/gcOthLP3+kePyzAy506dlFPr9D2Q+tOf9/+3de5BcZ33m8e+v+/R1em6am26WLYxkr3yXhMELxiYmMfZS9obFsXMxsOvgpCicStgly9amTBZCEXBtLSRggzcQQzbgBC9LiayNdivYmF2wZfkCaztY6GLZI0tz0dxnuqdv7/5xTvf09MxoWmpNj2bm+VRNndt73vP263H3o3fePgc8j8Qll9D+gTtJ7t5NcudOwq2nfjqiKzomR7OMnUzPHmkOtieGpikWK1MzpNpiNHfE2bS9neYOP0A3dyRo6YiTiIdxI9PkT6bJD2bID2XIvz5G/mSa7HiOyrFmi3t47TG8rgTx7e2E22N47XE/PLfFCMX1Ky8islY558A5HA5csI0LjlFxLDheWi8dxwV1VB+b54myCxwrb1fsd5T2VZVZcP/MzpmirqququOzzpld79z9ruqM03s9Cx1b+HXW/nqoOGXzjkvnXHM5KWGcDUOHwUINu0d1oVjg2b5neezVx3j8tcc5mTlJ2MLs7NnJx3d/nOvPu54tLaeeipIfHGRq3z4m9+1j6pn9ZA8dAsBiMRJXXknn7/++PxJ9xRWEkrNvE1gsFJkczTIxlGF8ODN7xHnQ31fMz/6fK9kapaUjTs/WVrbtjgfBOUFzR5zmdXEsXyQ/kCY3mCY/mKbw2hj55/uZOJlmbCo/q65QSxSvI078onV4HQm8jri/XBcnlNCvtMhScs7hikWcK1IsFqHoKAbb5WOln4qyrrJcsarsPHWW1mfX4ddTWYdfPijnSoGner3oZyRXLB+rLDP/OS4oT/l8KuqZe07lNarPOdU15mlLsYjD4Yp+4Fv8/IWu7WYFv8ogWB0Qg60gTAYxplR/xX/7ymMLnT9v+CydM0/dlcHLzSpXGXxLdTLrWHm9XOc8154v8MqKZxbiYw/vWe5mzKIEcjYMHfYDtVf/0wQX4pzjxcEXefTIo+x9dS8D6QESXoJrN13Lu7a8i2s3XUtrbOER5PzwMFP7nmHq6aeZ3Pc02YN+iA41NZHYtZPWW28lvnMXXLCd6WlIT+QYGc+S2TfExPBxxocyTAxnGB/KMDmSDd7sZySaIzR3JOja0syFO7vKo8yl0OxFw7iiozA2Tb4/TW5givwrQ+T6p+gbSFMcrxhvNvw5zJ0JEpd1zgrO4XVxQlFN0ZCl4ZyjWMhTzBcoFPIUC4Xgp2pfPk+xWKCYL/jLQgFXKFB0RYqFIq5YmFkGwbFYKJSXxWLletE/tzhTvly2opy/nGffAnXNPXfmGn5QrQqrVQG1WB1kg+01zQwzwyyEmf+hXto3c2z29vz7QxCcP1NPafv0z6kubyEP/6syFe0ov4RgX8XrKb228nGsfL5fHoIzYIHzK+uZfSw4v9yGoG4zv06bueZMH89z7fJ15r6u0muiVEvFtUvXKtW/UN2zvls0T90259hCdc+UC65U1b/lArP7bWbX3GPlxey65pw/65yK/qhu3ALHKv8bLf56Tv06Z6+exuupPnmB656rDyxTqD4bho8s2dSPsewY3z/0fR458AgHRw4SCUW4dtO13PSmm7hu83UkvMS85xXGxpjYt5/Rp55l+IVfMNF7kmw0RS65Ds77NQpXnkehuYtsKE56Ik/6lSzTz40A++bUFQobqfYYzeuC6Rnr4qTaY6TWxWlu94NzpGIusssVyA34I875FwcZHUiTH5giP5Auz3EGsHiYSHeS+PZ2vK4Eka4kXpc/4myevgy4krlikUI+H/zkKORzFPN58jl/Wcjlqo77+4ql9Yp9ldvFfH4m5AaBt1C1r5DP44oFCvmKcvk8hUJh4f0FPzC74jKHRjNCoTChUAgLz16GQiEsFCYUDhEKhzELlqGKZWhmOxyJECrVUV1nKDQTDkMhLGSEQiGw4DpmWMiwUDhYD82UDY6FQuGgvaGZMuX1ivNC/nXmlJuvDRaCUEXZimNz2xAK2lwqVx125w+pM+u1h9Q5oUtEZB4K1WfD0GG45NfPapWHRg7xjZe+wWNHHiNTyHBJxyXce8293HjBjbREWwB/VG1yZJqTxyYYPTHByZePMvLqIOMjOTIuRjaSAtsFnbugc6ZuM4hPR0hEIyRSITo2pUg0R0ikIiSao8SDZaJiOd/9lIvZAvn+KbIvDjLZP0X+xCS5/ikKI9Mzc54M/4uBXQliW1vxupNEuhJ4XUlCqYg+qM4y51wQRrPks1kKuRy57DSFXC7YzpLP5chnp8nnchSyM9uFXI58xXmzy2TnCcS5qkCcJx+E52Jh7j2/6xX2PEJhj5AX9pfhsB8eS+ueV962cJhwOIwXTQblPMLhcHl/qWwo7BGuqq+0Hvbm7gt5fj2zy4eDUBsE3lKwrQzE84TeOfuCoCkiIiuTQnW90sP+z1kYqXbO8Vz/c/z1i3/Nj3p/RDwc570Xvpfbtt/Gjo4dZDN5jv9ylJcOHKL/6BiDR0fJpGdG1kKFLPHpDE3RHJ3dHqktMVq2nUeyLUGyOUqiJUqiOUI8eXoPHXH5ItkTk+T7p8j1TZErheehzEx4DhuRrgTRLS1EdiXwupN4XUkinXEssrana7hikXwuS256mnx22l9OT5PLVi0rj1eUq9zn/1SG3+zscJzL1j1/0IvG8CIRwtGov4xE8aJRwpEInhchmkwS9jzCkQhhr/Tj+YEz4q+X9s3ajkQIeR6e5y/nHPc8Ql4ELyg3c8wP0/oHmIiInMsUqutVuvNH+9a6qnmh/wW++NwX2d+3n7ZYGx+54iPcftHtMBzj0FP9PPLifvqPjuGKYBRpzvTRPnyY1MQx2hJZOne+mc53vpWmt91COJU6oza4giM/GATnvinyfZP+8mQaStk9ZHidcaIbU0Su6sbrSRLpacLrSGDhlR96nHPkpjNkp6bIZtJk08FPJk02PRVsT5ELjk2np8iVjmcy84blfHb6jNrixWJEorFZSy9YxlMpvEi0HHy9aMwPvdGovz/YVxmOvXI4ngnJkYrzwpEoYU/hVURE5EwoVNdr6LC/PMOR6gPDB/jL5/6SJ3qfoCPewSeu/gTvbruZI/uGeOx/HGCkz3/ASrs3ygXHn6f1xM9pm+ql+eqdpG67jtQ77iRy/vmnHYSK6Ty545Nkj0+QOz7p//RNQumuHYb/BcGeJInLOomUwnNn4pyb71wsFMphN5uuCMOZ9OxwXA7JfjjOZaaCYJwmVzovk6ltpNeMaDxBNJEoLyPxBPGmJrxYfCYMB0F41nKesFx93ItEFW5FRERWEIXqepVHqi84rdMGpgb4wnNf4PuHvk8qkuKey/+Ad+Tewy/3DvLIL57HDDq9IS4++iM6ju0jESmQuu6dNH/4bpre+c6aR6Nd0VEYzgQBOgjPb0z4854DoaYIkQ1NpK7ZSGRDE5H1TUS6Eks2bcM550+HCEZ6s+n0zGhvxWjwqcPxzHn53DxPWJxH2POIJJIzYTiRJN7cQktXz0w4TiZnheVIIkksKBspn5cgEosr9IqIiEiZQnW9ho9A8waIJhcvC+SKOb71T9/igZ89QLaQ5UPb/w3XjN7MK383wOMjvyTpZblw8CesP/C/iHs5mt99A62f+DzJa64hFD31Lftc0ZEfTJM9NkGud9xfHp/ETQdfGjPwOhNEz28h8rYmIhuaiG5IEWo+vS8M5jIZ0hPjTE9NMj0xQWZqkunJCaYnJ8hMButTlaPGUxXTKPz1Wu+yEInFywG4FHSbOzpnBWN/f7IceKOzgnMiCMNJvDoenS4iIiJyKgrV9Ro6XPPUj6eOP8Vnn/4sh0cPc33nDdyS/iBHvzPOc1O9rMu9wYX/9D06Rl8h9fZraP3Mn9B8w6/MefBKiSs68ifT5I5NkO2dIHtsnNyxSVzWD9AWCRHZmCK5s7scnr2e5Cnv8VzI5xk/Ocho3wnGBvuZHBlmcmSYqZFhJkeHg+0Rcpn0KV9nNJEklmyaFXJT7R0zAbgcdBPEEkkiFVMoovEk0aS/jMRj/m27RERERM5xCtX1GjoMb/7VUxYZyYxw3/772HNoD+fHt3Jv5C8Y/gEcyA3TOfIylx7+n3Stg7YP307rLV/F6+iYdb5zjsLJDNljQXjunSB7bGJmBNoLEd3YRHJXN9FNzUQ3p/C6knO+OOicY2pslNG+E4z2n2C0v4+RvhOMDZxgpK+P8ZMDc0aQY01NNLW209TWTs+bttHU1k6ytY1EczPxphSxZIp4KkUs2UQslSKW8G9hJiIiIrKWKFTXY3ocJvpg3fx3/nDOsffoXj779GcZT09wd+iPSf50I/0ZR9fA82zt3cvGt19G2x/9J5JXv6U8BaM4nSf7+gTZ18bIvjZO9rUxiqVHdYfNH4G+qpvophSRzc1EuhNY2P/yYDY9xUh/H6PP9zPWf4LRgX5G+/vKIbp6lDnZ2kZrdw8bt19MW8/1tHT30Na9npaubpra1uEtMuVERERERBSq6zN4wF92XTTnUN9kH3/29J/xxGtP8Cvp93LFL95JejpGbOQgl488ydZ/dR1t7/s2XkcHhdFppl4YIPvqKNmj4/5dOIIbUIQ6otgFcULrjHyLI5eYZjwzzOToEaYOjDD1zIg/LWN0hPHBATIT47Pa4cVitHb10NqznvMuuYy27vW09qz393WvJxKPL3EniYiIiKx+CtX1GAhCdefsUP3Ykcf49FOfZtPx8/jDw/eSyXdg46+zo/AMre/YRrH7X3KkL0/kSz+kKdNMwjUBkHPTDGf7GMz0MpDu5eT0G+SOLHyP41DYK0/HaF7XwcZtF9HS1UNrdw8tXd20dq8n0dyiu1SIiIiILDGF6noMvgIhrzz9Yzw7zmee/gw/e+Y5fvvAByjkYqQzz+K5V7FoC9OprXiHNrCutweAvMsyFh5iIHaMqeQU+aYCkUSMeKybN8W2cHEiQSQe97/UF48TiQXLRIKm1nZiTU0KzCIiIiLngIaHajN7D/BFIAz8lXPuz6uOx4BvAruAk8DtzrlXG93OmgwcgHUXQjjC/hP7uW/Pp3jrT3dwY34XudwT9CTWs6ltG5ubbyBKHIcj1BMjuaOTph3dRDamVsVTCEVERETWuoaGajMLA18GfhXoBZ4xsz3OuZcrit0FDDvn3mxmdwCfA25vZDtrNvgKxa6L+dr/uZ/hr73AtdMbWR8vsrntIjY03UiYMBYLE7+onfjF64hvbyec0hf/RERERFabRo9UXw0cdM4dBjCzh4FbgcpQfSvwp8H6I8CXzMycq+XZ0Q2UzzI0+Bp///JbWZ8b4srmt9PTfT4hCxNqjpC4tJPEJR3EtraW78whIiIiIqtTo0P1JuD1iu1e4K0LlXHO5c1sFOgABhvSwhr99IFvEh/9Ev+iZQNmRs7L0XLNFhKXdRLd3IyFNK1DREREZK1odKieL2lWj0DXUgYzuxu4G2DLli31t+w0xTs8okdi9HKQKz/6PuKbWvWlQREREZE1qtGhuhc4r2J7M/DGAmV6zcwDWoGh6oqccw8CDwLs3r274VNDrvqtD5H7jRwRL9LoS4uIiIjIOabRk32fAbaZ2VYziwJ3AHuqyuwBPhisvx/44Tk3nzqgQC0iIiIi0OCR6mCO9EeBvfi31Pu6c+4lM/sUsN85twf4GvA3ZnYQf4T6jka2UURERETkdDX8PtXOuUeBR6v23VuxngFua3S7RERERETOlO71JiIiIiJSJ4VqEREREZE6KVSLiIiIiNRJoVpEREREpE4K1SIiIiIidVKoFhERERGpk0K1iIiIiEidFKpFREREROqkUC0iIiIiUieFahERERGROilUi4iIiIjUSaFaRERERKROCtUiIiIiInVSqBYRERERqZNCtYiIiIhIncw5t9xtqJuZDQBHl+nyncDgMl17NVO/Lh317dJR3y4d9e3SUd8uHfXt0lnOvj3fOddVvXNVhOrlZGb7nXO7l7sdq436demob5eO+nbpqG+Xjvp26ahvl8652Lea/iEiIiIiUieFahERERGROilU1+/B5W7AKqV+XTrq26Wjvl066tulo75dOurbpXPO9a3mVIuIiIiI1Ekj1SIiIiIidVKoroGZvcfMXjGzg2b2iXmOx8zs74LjT5vZBY1v5cpUQ99+zMxeNrOfm9k/mtn5y9HOlWixvq0o934zc2Z2Tn2L+lxWS9+a2W8Ev7svmdm3Gt3GlaqG94QtZva4mT0fvC/cvBztXInM7Otm1m9mLy5w3MzsL4K+/7mZ7Wx0G1eiGvr1t4P+/LmZ/cTMrmh0G1eqxfq2otxbzKxgZu9vVNvmo1C9CDMLA18GbgJ2AL9pZjuqit0FDDvn3gz8F+BzjW3lylRj3z4P7HbOXQ48Any+sa1cmWrsW8ysGfgD4OnGtnDlqqVvzWwb8B+AtzvnLgH+sOENXYFq/L39E+DvnXNXAXcA9ze2lSvaQ8B7TnH8JmBb8HM38EAD2rQaPMSp+/UIcF3wOfZpzsG5wOewhzh135beNz4H7G1Eg05FoXpxVwMHnXOHnXNZ4GHg1qoytwLfCNYfAW4wM2tgG1eqRfvWOfe4c24q2HwK2NzgNq5Utfzegv8G/3kg08jGrXC19O2HgS8754YBnHP9DW7jSlVL3zqgJVhvBd5oYPtWNOfck8DQKYrcCnzT+Z4C2sxsQ2Nat3It1q/OuZ+U3gvQ59hpqeF3FuAe4L8Dy/4+q1C9uE3A6xXbvcG+ecs45/LAKNDRkNatbLX0baW7gMeWtEWrx6J9a2ZXAec55/6hkQ1bBWr5vd0ObDez/2tmT5nZKUdapKyWvv1T4HfMrBd4FP8DVc6O031PltOnz7GzyMw2Ab8OfGW52wLgLXcDVoD5Rpyrb5lSSxmZq+Z+M7PfAXYD1y1pi1aPU/atmYXwpyp9qFENWkVq+b318P+Efj3+qNSPzexS59zIErdtpaulb38TeMg595/N7Brgb4K+LS5981Y9fZYtITN7F36ofsdyt2UV+QLw751zhXNhgoBC9eJ6gfMqtjcz98+NpTK9Zubh/0lysT9XSG19i5m9G/iP+HPSphvUtpVusb5tBi4FngjeiNYDe8zsFufc/oa1cmWq9T3hKedcDjhiZq/gh+xnGtPEFauWvr2LYI6lc+6nZhYHOjkH/vS7CtT0niynz8wuB/4KuMk5d3K527OK7AYeDj7HOoGbzSzvnPvecjRG0z8W9wywzcy2mlkU/4sxe6rK7AE+GKy/H/ih0w3Aa7Fo3wZTFL4K3KJ5qafllH3rnBt1znU65y5wzl2AP89Pgbo2tbwnfA94F4CZdeJPBznc0FauTLX07WvADQBm9s+AODDQ0FauXnuADwR3AXkbMOqcO77cjVrpzGwL8F3gTufcgeVuz2rinNta8Tn2CPCR5QrUoJHqRTnn8mb2UfxvlYaBrzvnXjKzTwH7nXN7gK/h/wnyIP4I9R3L1+KVo8a+vQ9IAd8J/iX6mnPulmVr9ApRY9/KGaixb/cCv2ZmLwMF4OManVpcjX37b4H/amZ/hD814UMaxKiNmX0bf0pSZzAn/ZNABMA59xX8Oeo3AweBKeBfL09LV5Ya+vVe/O9Z3R98juWdc7qFaQ1q6Ntzip6oKCIiIiJSJ03/EBERERGpk0K1iIiIiEidFKpFREREROqkUC0iIiIiUieFahERERFZEczs62bWb2YvnqX6fmBmI2b2D1X7/9bMXjGzF4NrRharS6FaRERERFaKhwgeAHWW3AfcOc/+vwUuBi4DEsDvLlaRQrWIyBpkZh8zM2dmv7XcbRERqZVz7kmqnlptZhcGI87PmtmPzezi06jvH4HxefY/6gLAPvwnjJ6SQrWIyNq0M1g+u6ytEBGp34PAPc65XcC/A+4/WxUH0z7uBH6wWFk9UVFEZG3aBUwAv1zuhoiInCkzSwH/nJknLwPEgmPvAz41z2nHnHM31niJ+4EnnXM/XqygQrWIyBpiZp8D/rhiV6Hig+hO59x/a3yrRETOWAgYcc5dWX3AOfdd4LtnWrGZfRLoAn6vlvIK1SIia8uzwDeADwI/Af53xbEfLUuLRETOkHNuzMyOmNltzrnvmD9KcLlz7mf11GtmvwvcCNzgnCvWdI4//1pERNYKM7sb+Crwe865B5e7PSIitTKzbwPXA51AH/BJ4IfAA8AGIAI87Jybb9rHfPX9GP8uHyngJHCXc26vmeWBo8x8ifG7i9WpUC0issaY2Vfw/5z5Fufc/uVuj4jIaqC7f4iIrD07gRzw/5a7ISIiq4VCtYjIGmJmHv7DDF52zk0vd3tERFYLhWoRkbVlBxAHnlvuhoiIrCYK1SIia0vptlPPL2srRERWGYVqEZG1pSNYji1rK0REVhndp1pEZG0pPZb8M2Z2KTAJvOSc+84ytklEZMXTSLWIyBrinHsSuAc/TN+Df4/XOU8iExGR06P7VIuIiIiI1Ekj1SIiIiIidVKoFhERERGpk0K1iIiIiEidFKpFREREROqkUC0iIiIiUieFahERERGROilUi4iIiIjUSaFaRERERKROCtUiIiIiInVSqBYRERERqdP/B/4Qy2GNmJKDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#To be more accurate let us use 300 Kelvin as the temperature\n",
    "Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "lam = 35 * 3e10 * 2 * pi  #35 cm^-1\n",
    "gamma = (1/(50e-15))   #1/50 fs\n",
    "tlist = linspace(0,1.4e-12,1000)\n",
    "\n",
    "beta = 1/Temperature\n",
    "DL = \" 2*pi* 2.0 * {lam} / (pi * {gamma} * {beta})  if (w==0) else 2*pi*(2.0*{lam}*{gamma} *w /(pi*(w**2+{gamma}**2))) * ((1/(exp((w) * {beta})-1))+1)\".format(gamma=gamma, beta = beta, lam = lam)\n",
    "\n",
    "optionsODE = Options(nsteps=15000, store_states=True,rtol=1e-12,atol=1e-12)\n",
    "outputBR  =  brmesolve(H, psi0, tlist, a_ops=[[Q,DL] for Q in Q_list], options = optionsODE)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1,1, figsize=(12,8))\n",
    "for m,Q in enumerate(Q_list):\n",
    "    axes.plot(tlist, expect(outputBR.states,Q),label=m+1)\n",
    "#for m,Q in enumerate(Q_list):\n",
    "#    axes.plot(tlist, expect(outputFMO.states,Q),linestyle=\"--\",label=m+1)\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"Population\", fontsize=16);\n",
    "\n",
    "axes.set_title('Bloch Redfield solution ',fontsize=24)\n",
    "axes.legend(loc=0, fontsize=18)\n",
    "fig.savefig(\"fmoBR.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Not too dissimilliar time-scales appear...  but is our approach valid here?  If the memory time of the bath is between $50$ and $200$ fs, and the coupling strength is of the order of 35 cm$^{-1}$, both values that may violate the Born-Markov approximations.\n",
    "\n",
    "<center>\n",
    "<img src=\"fmoexperiment.png\" height=\"600\" width=\"600\"/>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion\n",
    "\n",
    "- Comparing different methods\n",
    "- Evaluating efficiency\n",
    "- Conclusions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Non-Markovian systems\n",
    "\n",
    "In other situations the assumption that $\\tau_E \\ll \\tau_S, \\tau_R$ also breaks down. E.g.,\n",
    "\n",
    "- Molecular systems strongly interacting with their environment, e.g., energy transfer in photosynthetic complexes strongly couples to protein \"vibrations\".\n",
    "- Hyperfine Interaction between electron spins and nuclear spins in quantum dots \n",
    "- Superconducting qubits strongly coupled to open transmission lines\n",
    "- Recent evidence suggests signifcant non-Markovian noise in IBM-Q simulations\n",
    "\n",
    "\n",
    "A recent review:\n",
    "\"Dynamics of non-Markovian open quantum systems\"\n",
    "Inés de Vega and Daniel Alonso\n",
    "Rev. Mod. Phys. 89, 015001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Bosonic environments\n",
    "\n",
    "The choice of a bosonic environment, or in general, a Gaussian environment, simplifies the problem to some degree.  \n",
    "\n",
    "Using the fact that the cumulants of a <span style=\"color:red\">Gaussian</span> system truncate at second order, one can show (see Breur and Petruccione, 3.6.4, or Jian Ma et al, PRA 2012) that there is a formal solution (assuming that at $t=0$, $\\rho(0) = \\rho_S(0)\\otimes \\rho_E(0)$ ),\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ \\tilde{\\rho}_S(t) = \\mathcal{T} \\exp\\left( - \\int_0^t dt_2 \\int_0^{t_2} A^{\\times}(t_2)[C^R(t_2-t_1) A(t_1)^{\\times} + i C^I(t_2-t_1)A(t_1)^{\\circ}]\\right)\\rho_S(0) $$\n",
    "\n",
    "Where, as before $A(t)$ is the system operator which couples to the environment, \n",
    "\n",
    "$C(t)$ is the correlation function of the environment, split into real and imaginary parts, \n",
    "\n",
    "$A^{\\times}B \\equiv [A,B]$ and $A^{\\circ}B = \\{A,B\\}$.  \n",
    "\n",
    "$\\mathcal{T}$ is the time-ordering operator, which means that all terms have to reordered so that time arguments increase from right to left.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Directly solving or using this equation is intractable;  however, by assuming that we can write the correlation functions as a sum of exponentials, and taking repeated time-derivatives, one can derive the <span style=\"color:red\">hierarchy equations of motion.</span>\n",
    "\n",
    "Again assuming that the initial bath state is a thermal state, and recalling that \n",
    "\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "we can rewrite  this as\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega J(\\omega)\\left[ \\mathrm{coth}\\left(\\frac{\\beta\\omega}{2}\\right)\\cos \\left(\\omega t\\right) - i \\sin \\left(\\omega t)\\right)\\}\\right]$$\n",
    "\n",
    "$\\beta = 1/ k_B T$, the temperature of the initial environment state.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The fact that the environment is fully described by 2nd order correlation functions allows us to identify important degrees of freedom in the environment, and include them in the simulation.  We then can have a model which captures quantum effects (coherence/entanglement between system and environment).\n",
    "\n",
    "For some choices of spectral density, this does have the analytical form of a sum of exponentials, e.g. a Lorentzian.  Traditionally, the Drude-Lorentz form is chosen,\n",
    "\n",
    "$$J(\\omega) = \\frac{\\omega}{\\pi} \\frac{2\\lambda \\gamma}{(\\gamma^2 + \\omega^2)} $$\n",
    " \n",
    "Inserting this into $C(\\tau)$ one finds,\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(\\tau) = \\sum_{k=0}^{\\infty} c_k e^{-v_k|\\tau|}$$\n",
    "\n",
    "\n",
    "Where $v_k = 2 \\pi k/\\beta$ for $k\\geq1$, and $v_0 = \\gamma$, and $c_0 = \\lambda \\gamma [-i + \\mathrm{cot}\\left(\\beta \\gamma /2\\right)]$ and $c_k = (4 \\lambda \\gamma/\\beta) v_k/(v_k^2 - \\gamma^2)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def cot(x):\n",
    "    return 1./np.tan(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "E.g., for the parameters given before $\\gamma =1/50$ fs, $\\lambda = 35$ cm$^{-1}$, $T$ =  300K\n",
    "\n",
    "<center>\n",
    "<img src=\"drude.png\" width=1200 /> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def c(t):\n",
    "    c_temp =[]\n",
    "    c_temp.append(lam * gamma * (-1.0j + cot(gamma / (2 * T))) * np.exp(-gamma * t))\n",
    "    for k in range(1,5):\n",
    "        vk = 2 * np.pi * k * T\n",
    "        c_temp.append( (4 * lam * gamma * T * vk / (vk**2 - gamma**2))  * np.exp(- vk * t) ) \n",
    "    return c_temp\n",
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/( pi* ((energy**2) + (gamma**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/neill/anaconda3/lib/python3.7/site-packages/numpy/core/_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#A quick plot of the spectral density and environment correlation functions\n",
    "\n",
    "wlist = linspace(0, 200*3e10*2*pi,100)\n",
    "lam = 35 * 3e10 * 2 * pi\n",
    "gamma = (1/(50e-15))\n",
    "T = Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "\n",
    "#gamma = 1.0\n",
    "\n",
    "#lam = 2.5/2.\n",
    "\n",
    "#T = 1/0.95\n",
    "tlist = linspace(0,1.4e-12,1000)\n",
    "\n",
    "\n",
    "J = [J0(w)/(3e10*2*pi) for w in wlist]\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, sharex=False, figsize=(10,3))\n",
    "\n",
    "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
    "\n",
    "axes[0].plot(wlist/(3e10*2*pi), J, color='r',ls='--')\n",
    "axes[0].set_xlabel(r'$\\omega$ (cm$^{-1}$)', fontsize=20)\n",
    "axes[0].set_ylabel(r\"$J(\\omega)$ (cm$^{-1}$)\", fontsize=16);\n",
    "axes[1].plot(tlist, [np.real(sum(c(t))) for t in tlist], color='r',ls='--',label=\"c(t) real\")\n",
    "axes[1].plot(tlist, [np.imag(sum(c(t))) for t in tlist], color='g',ls='--',label=\"c(t) imaginary\")\n",
    "axes[1].plot(tlist, [c(t)[0] for t in tlist], color='b',ls='--',label=\"k=0 real\")\n",
    "axes[1].plot(tlist, [c(t)[1] for t in tlist], color='y',ls='--',label=\"k=1 real\")\n",
    "axes[1].set_xlabel(r'$t$', fontsize=20)\n",
    "axes[1].set_ylabel(r\"$C(t)$\", fontsize=16);\n",
    "\n",
    "axes[1].legend(loc=0)\n",
    "\n",
    "fig.savefig(\"drude.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Given these assumptions (<span style=\"color:red\">seperable initial condition, bosonic environment initially in a thermal state</span>), one can derive the <span style=\"color:blue\">Tanimura and Kubo HEOM</span>, which looks like the following\n",
    "\n",
    "$$\\dot{\\rho}^n(t) = -(iH_S^{\\times} + \\sum_{k=0}^M\\, n_k \\,v_k)\\,\\rho^{n}(t)$$\n",
    "$$ - i \\sum_{k=0}^M\\, A^{\\times}\\, \\rho^{n^+_k}(t)$$\n",
    "$$ -i  \\sum_{k=0}^M n_k(c_k\\, A\\,\\rho^{n^-_k}(t) - c_k^*\\,\\rho^{n^-_k}(t)\\, A)$$\n",
    "\n",
    "This is a set of coupled equations for a hierarchy of \"density matrices\" labelled by an index $n$.  \n",
    "\n",
    "In this case $n = \\{n_1,n_2,..n_m,...,n_M\\}$: it contains M indices, $0$ to $M$, a cut-off in the number of exponentials.  \n",
    "\n",
    "Each element runs from $0$ to $N_c$, an additional cut-off term.\n",
    "\n",
    "$n^+_k$ means one increases the $k$th component of $n_k$ by $1$, while  $n^-_k$ means decrease by $1$. $n= \\{0,0,0,..0\\}$ denotes the physical density matrix. All the rest are \"auxiliary\" non-normalized density matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing BMS master equation and the HEOM\n",
    "\n",
    "Before looking again at the FMO example, lets try and see the breakdown of the BMS (Born-Markov-Secular) master equation as we increase the bath correlation time with some simpler (unitless) parameters, and with just a 2-level system.\n",
    "\n",
    "First try lets try some parameters where BMS should work (in units of system emergy $\\epsilon$):\n",
    "\n",
    "$\\gamma=10 \\epsilon$  $\\quad$ Very large: short memory time, Markovian\n",
    "\n",
    "$\\lambda = 0.05 \\epsilon$  $\\quad$ Very weak: Born approximation should be valid.\n",
    "\n",
    "$\\beta = \\epsilon$  $\\quad$ Overall dissipation rate not too large because of temperature? Secular approximation should be ok."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Calculates  generic non-secular master equation\n",
    "#This is experimental, and should be used with a grain of salt\n",
    "\n",
    "\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "from numpy import matrix\n",
    "from numpy import linalg\n",
    "from qutip import spre, spost, sprepost, thermal_dm, mesolve, Odeoptions\n",
    "from qutip import tensor, identity, destroy, sigmax, sigmaz, basis, qeye, dims\n",
    "from qutip.ui.progressbar import BaseProgressBar, TextProgressBar\n",
    "def Lnonsec(Hsys, Q, tlist, initial_state, Temperature,\n",
    "            return_vals, eigen_sparse=False, options=None,progress_bar=None):\n",
    "    \n",
    "\n",
    "    if progress_bar is None:\n",
    "        progress_bar = BaseProgressBar()\n",
    "    elif progress_bar is True:\n",
    "        progress_bar = TextProgressBar()\n",
    "        \n",
    "    if options is None:\n",
    "        options = Options()\n",
    "    output = None\n",
    "    \n",
    "    dot_energy, dot_state = Hsys.eigenstates(sparse=eigen_sparse)\n",
    "    deltaE = dot_energy[1] - dot_energy[0]\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    dimensions = dims(Q)\n",
    "    Nmax = dimensions[1][0]        #hilbert space \n",
    "    #Nmax = 2       #hilbert space \n",
    "    \n",
    "    H = Hsys\n",
    "    L=0\n",
    "    PsipreEta=0\n",
    "    PsipreX=0\n",
    "\n",
    "    all_energy, all_state = H.eigenstates(sparse=eigen_sparse)\n",
    "    Apre = spre(Q)\n",
    "    Apost = spost(Q)\n",
    "    for j in range(Nmax):\n",
    "        for k in range(Nmax):\n",
    "            A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            delE = (all_energy[j] - all_energy[k])\n",
    "            if np.absolute(A) > 0.0:\n",
    "                if abs(delE) > 0.0:\n",
    "                    #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                    X = (0.5  * np.pi * J0(all_energy[j] - all_energy[k])\n",
    "                         * (np.cosh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature))\n",
    "                         / (np.sinh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature)))) * A)\n",
    "                    #eta = (0.5 * np.pi * gamma *\n",
    "                    eta = (0.5 *  np.pi *\n",
    "                           J0(all_energy[j] - all_energy[k]) * A)\n",
    "                    PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                    PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                             * all_state[k].dag())\n",
    "                else:\n",
    "                    #X =0.5  * np.pi* J0(0.) * A * 2 * Temperature\n",
    "                    X =0.5  * np.pi* J02(0.)* A  * 2 * Temperature\n",
    "                    #X =0.5 * np.pi * gamma * A * 2 * Temperature\n",
    "                    PsipreX=PsipreX+X*all_state[j]*all_state[k].dag()\n",
    "\n",
    "    A = Q\n",
    "    L = ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "         +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "         +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "         +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "\n",
    "    #Setup the operators and the Hamiltonian and the master equation \n",
    "    #and solve for time steps in tlist\n",
    "    psi0 = ( initial_state)\n",
    "    output = mesolve(H, psi0, tlist, [L], return_vals, options=options,progress_bar=progress_bar)\n",
    "    \n",
    "    return output\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmax()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmaz()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = 0.05           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "psi0=basis(2,0)\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 10\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "\n",
    "def nbs(energy,Temperature):\n",
    "    beta = 1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n",
    "\n",
    "(recall everything here is in units of $\\epsilon=1$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "173.54646467436356\n"
     ]
    }
   ],
   "source": [
    "print(1/(np.pi * J0(1.0) * nbs(1.0,temperature)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.15915494309189535\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_E \\ll \\tau_S \\ll \\tau_R$ for the Born-Markov-Secular approximation seems valid. Let's check.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True,)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "beta = 1/temperature\n",
    "DL = \" 2*pi* 2.0 * {lam} / (pi * {gamma} * {beta})  if (w==0) else 2*pi*(2.0*{lam}*{gamma} *w /(pi*(w**2+{gamma}**2))) * ((1/(exp((w) * {beta})-1))+1)\".format(gamma=gamma, beta = beta, lam = lam)\n",
    "\n",
    "optionsODE = Options(nsteps=15000, store_states=True,rtol=1e-12,atol=1e-12)\n",
    "outputBR  =  brmesolve(Hsys, rho0, tlist, a_ops=[[sigmaz(),DL]], options = optionsODE)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    "plus =  (basis(2,0)+basis(2,1))/np.sqrt(2.) \n",
    "minus = (basis(2,0)-basis(2,1))/np.sqrt(2.) \n",
    "smt = minus*plus.dag()\n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1))*smt,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*smt.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"heom1.png\" width=800 /> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f53527b47b8>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1p=rho0\n",
    "psi01 = basis(2,1)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "P1BR=expect(outputBR.states,P1p)\n",
    "P12BR=expect(outputBR.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch Redfield solver\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "axes1.set_title('$\\lambda=0.05 \\epsilon $, $\\gamma = 10 \\epsilon $, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch-Redfield\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "#fig.savefig(\"heom1.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Next try lets try some parameters where BMS should break, \n",
    "\n",
    "$\\gamma=0.1 \\epsilon$  $\\quad$ Narrow environment, long memory time... Non-Markovian...\n",
    "\n",
    "$\\lambda = 0.2 \\epsilon$  $\\quad$ Large coupling, Born-approximation breaks.\n",
    "\n",
    "$\\beta = \\epsilon$  $\\quad$ Same as before..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmax()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmaz()\n",
    "\n",
    "\n",
    "gamma = .1                # Cutoff frequency of DL spectral density\n",
    "lam = 0.2           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "Ncut = 25\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.386616168590876\n"
     ]
    }
   ],
   "source": [
    "print(1./(np.pi*J0(1.0)*nbs(1.0,temperature)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "0.15915494309189535\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_S \\ll \\tau_R$ seems ok, but now $\\tau_E > \\tau_S$, so Markov approximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*smt,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*smt.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "DL = \" 2*pi* 2.0 * {lam} / (pi * {gamma} * {beta})  if (w==0) else 2*pi*(2.0*{lam}*{gamma} *w /(pi*(w**2+{gamma}**2))) * ((1/(exp((w) * {beta})-1))+1)\".format(gamma=gamma, beta = beta, lam = lam)\n",
    "\n",
    "optionsODE = Options(nsteps=15000, store_states=True,rtol=1e-12,atol=1e-12)\n",
    "outputBR  =  brmesolve(Hsys, rho0, tlist, a_ops=[[sigmaz(),DL]], options = optionsODE)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"heom2alt.png\" width=800 />\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/neill/anaconda3/lib/python3.7/site-packages/numpy/core/_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f535219def0>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "#psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "psi01 = basis(2,1)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "P1BR=expect(outputBR.states,P1p)\n",
    "P12BR=expect(outputBR.states,P12p)\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch Redfield\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.2 \\epsilon$, $\\gamma = 0.1 \\epsilon$, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch redfield\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "#fig.savefig(\"heom2alt.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next try lets try some parameters where secular approximation should break, but Born-Markov is ok \n",
    "\n",
    "$\\gamma=10 \\epsilon$  $\\quad$\n",
    "As before (Markovian)\n",
    "\n",
    "$\\lambda = 0.5 \\epsilon$  $\\quad$ \n",
    "Strong coupling..\n",
    "\n",
    "$\\beta = 0.25\\epsilon$  $\\quad$\n",
    "Large temperature..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmax()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmaz()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = .5           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 4.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=basis(2,0)\n",
    "#psi0=basis(2,0)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 20\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2341120909788104\n"
     ]
    }
   ],
   "source": [
    "print(1./(np.pi*J0(1.0)*(nbs(1.0,temperature)+1.)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.039788735772973836\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so now $\\tau_R \\approx \\tau_S$, so Secular appoximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*smt,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*smt.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "beta = 1/temperature\n",
    "DL = \" 2*pi* 2.0 * {lam} / (pi * {gamma} * {beta})  if (w==0) else 2*pi*(2.0*{lam}*{gamma} *w /(pi*(w**2+{gamma}**2))) * ((1/(exp((w) * {beta})-1))+1)\".format(gamma=gamma, beta = beta, lam = lam)\n",
    "\n",
    "optionsODE = Options(nsteps=15000, store_states=True,rtol=1e-12,atol=1e-12)\n",
    "outputBR  =  brmesolve(Hsys, rho0, tlist, a_ops=[[sigmaz(),DL]], options = optionsODE)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"heom4.png\" width=800 />\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/neill/anaconda3/lib/python3.7/site-packages/numpy/core/_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "psi01 = (basis(2,1))\n",
    "\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "P1BR=expect(outputBR.states,P1p)\n",
    "P12BR=expect(outputBR.states,P12p)\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch Redfield\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation nonsecular \")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.5 \\epsilon$, $\\gamma = 10 \\epsilon$, $k_{B}T=4\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation Secular\")\n",
    "axes2.plot(tlist , P12BR,  color=\"blue\", ls=\"-.\", alpha=1, linewidth=2.0,label=\"Bloch Redfield\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "fig.savefig(\"heom4.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The HEOM and FMO\n",
    "\n",
    "Let us return back to the FMO result. We saw the simulation from our Lindblad model already.\n",
    "\n",
    "Similarly, lets use the same spectral density and temperature in the HEOM model.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(5.072528597792653e+26+0j)]\n",
      "[(-1.3194689145077131e+26+0j)]\n",
      "[(20000000000000+0j)]\n",
      "[(20000000000000+0j)]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/mnt/e/Dropbox/Dropbox/talks/todai talk 2020/heom_fmotd_NL.py:244: UserWarning: Expected simplified input.\n",
      "  warnings.warn(\"Expected simplified input.\")\n",
      "/mnt/e/Dropbox/Dropbox/talks/todai talk 2020/heom_fmotd_NL.py:249: UserWarning: Expected simplified input.\n",
      "  warnings.warn(\"Expected simplified input.\")\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "from heom_fmotd_NL import BosonicHEOMSolver\n",
    "\n",
    "\n",
    "Hsys =  3e10 * 2 * pi *Qobj([[200, -87.7, 5.5, -5.9, 6.7, -13.7, -9.9],\n",
    "                    [-87.7, 320, 30.8, 8.2, 0.7, 11.8, 4.3],\n",
    "                    [5.5, 30.8, 0, -53.5, -2.2, -9.6, 6.0],\n",
    "                    [-5.9, 8.2, -53.5, 110, -70.7, -17.0, -63.3],\n",
    "                    [6.7, 0.7, -2.2, -70.7, 270, 81.1, -1.3],\n",
    "                    [-13.7,11.8, -9.6, -17.0 ,81.1, 420, 39.7],\n",
    "                    [-9.9, 4.3, 6.0, -63.3, -1.3, 39.7, 230]])\n",
    "\n",
    "\n",
    "#start the excitation at site :1:\n",
    "rho0 = basis(7,0)*basis(7,0).dag() \n",
    "\n",
    "#time...  .15 = how many ps?  around 1, but need to get units correct\n",
    "tlist = linspace(0,1.4e-12,1000)\n",
    "eigen_sparse = False\n",
    "calc_time = True                                             \n",
    "\n",
    "# might as well use Q as projectors for site populations for plotting, but whatever\n",
    "P1=basis(7,0) * basis(7,0).dag()\n",
    "P2=basis(7,1) * basis(7,1).dag()\n",
    "\n",
    "optionsODE = Options(nsteps=15000, store_states=True,rtol=1e-17,atol=1e-17)\n",
    "#\n",
    "Nc = 4\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk = 1\n",
    "#version with all bath parameters the same\n",
    "lam = 35 * 3e10 * 2 * pi\n",
    "gamma = (1/(50e-15))\n",
    "T = Temperature = 300 * 0.6949 * 3e10 * 2 * pi\n",
    "\n",
    "beta = 1/T\n",
    "\n",
    "pref = 1\n",
    "\n",
    "ckAR = [pref * lam * gamma * (cot(gamma / (2 * T))) + 0.j]\n",
    "ckAR.extend([(pref * 4 * lam * gamma * T *  2 * np.pi * k * T / (( 2 * np.pi * k * T)**2 - gamma**2))+0.j for k in range(1,Nk)])\n",
    "\n",
    "vkAR = [gamma+0.j]\n",
    "vkAR.extend([2 * np.pi * k * T + 0.j for k in range(1,Nk)])\n",
    "\n",
    "ckAI = [pref * lam * gamma * (-1.0) + 0.j]\n",
    "\n",
    "vkAI = [gamma+0.j]\n",
    "\n",
    "print(ckAR)\n",
    "print(ckAI)\n",
    "print(vkAR)\n",
    "print(vkAI)\n",
    "\n",
    "Q=[basis(7,m)*basis(7,m).dag() for m in range(7)  ]\n",
    "\n",
    "NR = len(ckAR)\n",
    "NI = len(ckAI)\n",
    "Q2 = []\n",
    "ckAR2 = []\n",
    "ckAI2 = []\n",
    "vkAR2 = []\n",
    "vkAI2 = []\n",
    "for m in range(7):\n",
    "    Q2.extend([ basis(7,m)*basis(7,m).dag() for kk in range(NR)])\n",
    "    ckAR2.extend(ckAR)    \n",
    "    vkAR2.extend(vkAR)\n",
    "   \n",
    "for m in range(7):\n",
    "    Q2.extend([ basis(7,m)*basis(7,m).dag() for kk in range(NI)])\n",
    "    ckAI2.extend(ckAI)\n",
    "    vkAI2.extend(vkAI)\n",
    "    \n",
    "\n",
    "\n",
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "\n",
    "HEOMMats = BosonicHEOMSolver(Hsys, Q2, ckAR2, ckAI2, vkAR2, vkAI2, Nc, options=options)\n",
    "outputFMOHEOM=HEOMMats.run(rho0,tlist)\n",
    "\n",
    "#P1HEOM=expect(output.states,P1)\n",
    "#P2HEOM=expect(output.states,P2)\n",
    "#P1HEOM=expect(output.states,P1)\n",
    "#P2HEOM=expect(output.states,P2)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,1, figsize=(12,8))\n",
    "for m in range(7):\n",
    "    Q =  basis(7,m)*basis(7,m).dag()\n",
    "    axes.plot(tlist, expect(outputFMOHEOM.states,Q),label=m+1)\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"Population\", fontsize=16);\n",
    "\n",
    "\n",
    "axes.set_title('HEOM solution ',fontsize=24)\n",
    "axes.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "fig.savefig(\"fmoheom.png\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "A | B | C\n",
    "- | - | - \n",
    "<img src=\"fmoheom.png\" alt=\"Drawing\" style=\"width: 550px;\"/> | <img src=\"fmosec2.png\" alt=\"Drawing\" style=\"width: 550px;\"/> |<img src=\"fmononsec2.png\" alt=\"Drawing\" style=\"width: 550px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A | B \n",
    "- | -  \n",
    "<img src=\"fmoheom.png\" alt=\"Drawing\" style=\"width: 550px;\"/> | <img src=\"fmoBR.png\" alt=\"Drawing\" style=\"width: 550px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How can we capture which model predicts a better long-time efficiency of energy transport?\n",
    "\n",
    "Let's return back to our two-level example (these results are from J. Chem. Phys. (2016), Illes-Smith, Dijkstra, Lambert and Nazir).\n",
    "\n",
    "$$H_S = \\frac{\\epsilon}{2} \\sigma_z + \\frac{\\Delta}{2}\\sigma_x$$  \n",
    "\n",
    "where the eigenstates of $\\sigma_z$ represent the position of the excitation on the two chromophores, $\\sigma_z = |X_1, 0_2 \\rangle \\langle X_1,0_2| -|0_1,X_2\\rangle \\langle 0_1,X_2|$\n",
    "\n",
    "<center>\n",
    "<img src=\"simple3.png\"/>    \n",
    "</center>\n"
   ]
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    "Efficiency relies on how quickly the excitation is moved from one chromophore to another (ultimately so that it can be moved to a reaction center).\n",
    "\n",
    "We can evaluate the dynamics of different models, and fit the long-time behavior to a rate:\n",
    "\n",
    "$$\\frac{dP_1(t)}{dt} = -k_{1\\rightarrow2} P_1 + k_{2\\rightarrow 1}P_2$$\n",
    "$$\\frac{dP_2(t)}{dt} = k_{1\\rightarrow2} P_1 -k_{2\\rightarrow 1}P_2$$\n",
    "\n"
   ]
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    "\n",
    "\n",
    "A | B\n",
    "- | - \n",
    "<img src=\"rates1.png\" alt=\"Drawing\" style=\"width: 550px;\"/>| <img src=\"rates2.png\" alt=\"Drawing\" style=\"width: 450px;\"/>"
   ]
  },
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   "source": [
    "We can also evaluate this for spectral densities with broad background and resonant structures:\n",
    "\n",
    "<center>\n",
    "    <img src=\"rates4.png\" alt=\"Drawing\" style=\"width: 900px;\"/> \n",
    "</center>\n",
    "\n"
   ]
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   "source": [
    "# Conclusions\n",
    "\n",
    "The study of open quantum systems lets us model how a system interacts with it environment in various limits:\n",
    "\n",
    "- Weak coupling, no bath memory (Markov), and weak damping gives us the Lindblad Born-Markov-Secular master equation\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "- Exact methods (HEOM, reaction coordinate, pseudo-modes (Lambert et al, Nat. Comm. 2019) give insight into strongly correlated system-bath problems when this approximation no longer holds, and everything occurs on comparable time-scales\n",
    "$$\\tau_E \\approx \\tau_S \\approx \\tau_R$$\n",
    "\n"
   ]
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   "source": [
    "\n",
    "\n",
    "\n",
    "### How does this help us study light-harvesting?\n",
    "\n",
    "- Comparing exact models, approximate models, and experimental data gives us insight more than each one alone.\n",
    "\n",
    "- E.g., in this example we saw that while the noise suppresses coherent oscillations, non-Markovian (resonant) environments can speed-up the transfer time of electronic energy across the whole complex,  which may be important for improving efficency.\n",
    "\n",
    "**All of these tools are useful for studying in noise in any type of quantum system;  quantum computers, quantum optics, condensed matter systems, etc, (cats?)**\n",
    "\n",
    "\n",
    "nwlambert@gmail.com"
   ]
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   "source": [
    "# Generalizing the spectral density\n",
    "\n",
    "The Drude-Lorentz spectral density is convenient because we can <span style=\"color:red\">analytically expand it as exponentials </span>.\n",
    "\n",
    "In other cases, we can <span style=\"color:red\">numerically calculate</span> the correlation functions, and then <span style=\"color:red\">numerically fit</span> them to a sum of exponentials.\n",
    "\n",
    "As a simple example, we can bench-mark against the analytically solvable \"pure dephasing model\", i.e., we set the coupling operator equal to the system Hamiltonian \n",
    "\n",
    "(see A. fruchtman, N. Lambert, E. Gauger, Scientific Reports 2016 for more interesting examples)"
   ]
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   "source": [
    "<img src=\"ohmic.png\" />"
   ]
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     "slide_type": "slide"
    }
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   "source": [
    "<img src=\"superohmic.png\" />"
   ]
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