Bragg cavity spectroscopy

[LorenzoFioroni]

This PR adds to TorchGPE the code used to study the roton-mode softening at the onset of self-organization

[JustStefaniak]

1. Shouldn't we remove line 259?
2. For real time evolution 260 will work, however for the imaginary time evolution we have "time"=None, which causes problems with callable cavity_probe(). I agree that it is not so useful in the imaginary time but we can allow in the imaginary time evolution to have stationary probes that do not change in time; constant cavity_probe(). That's why initially I had if clause discriminating with None value for the time and two different way of cavity_probe being calculated.

[JustStefaniak]

Comments for the get alpha implementation.

[LorenzoFioroni]

1. Shouldn't we remove line 259?

Yes, you are right. Thanks

2. For real time evolution 260 will work, however for the imaginary time evolution we have "time"=None, which causes problems with callable cavity_probe(). I agree that it is not so useful in the imaginary time but we can allow in the imaginary time evolution to have stationary probes that do not change in time; constant cavity_probe(). That's why initially I had if clause discriminating with None value for the time and two different way of cavity_probe being calculated.

In line 207 we define self._cavity_probe = time_dependent_variable(self.cavity_probe). This means that if its value is constant, self._cavity_probe will be a function mapping any input to the constant value self.cavity_probe. Hence, I would argue that even if time is None everything should work. Am I mistaken?