- Python scripts to animate a pair of 3D surfaces of revolution, and calculate their first and second derivatives.
Bushing's function is derived from the coherent states of the anisotropic harmonic oscillator.
γ(a, x) and Γ(a) are the lower incomplete gamma function, and gamma function respectively (see wolfram).
θ ranges from 0 to 2π in bushing's function, and from 0 to π for the surface of revolution.
The functions α(θ) and β(θ) are given by either
- cigar harmonic oscillator:
α(θ) = η^2sin^2(θ) and β(θ) = η^2cos^2(θ)
- pancake harmonic oscillator:
α(θ) = η^2cos^2(θ) and β(θ) = η^2sin^2(θ)
Note: The surface of revolution and its derivatives are wholly described by the parameters (η, λ, nF).
η (float): gaussian spread parameter
λ (int): anisotropy parameter
nF (int): occupancy parameter
For chosen values of (λ,nF) bushing's surfaces are animated for a range of η values.
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Th. Busch, J. R. Anglin, J. I. Cirac and P. Zoller, ”Inhibition of spontaneous emission in Fermi gases”, Euro-phys. Letters 44, 1 (1998). (doi)
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B. O'Sullivan & Th. Busch, ”Spontaneous Emission in ultra-cold spin-polarised anisotropic Fermi Seas”, Phys. Rev. A 79, 033602 (2009). (arXiv:0810.0231 | doi)
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Brian O'Sullivan, ”Spatial and energetic mode dynamics of cold atomic systems” PhD thesis (2012). (cora)
- see chapter 2.3 for a derivation of bushing's equation (2.112).