#230 Setup general Lindblad equation

[Ulf Lorenz]

What and Why

The paper https://arxiv.org/pdf/2004.01469.pdf seems to present an interesting way to setup a general Lindblad equation.

There may still be surprises, e.g., that you do not end up in thermal equilibrium, but at least you can reduce the problem of setting up a Lindblad operator to the problem of setting up the spectral density.

Acceptance criteria

• I understand the paper, maybe have the published reference
• There is a utility function that, given coupling operator, spectral density etc. as input generates the Lindblad Liouvillian.
• There are a few utility functions to generate simple spectral densities
  • ideas: Ohmian spectral density, Lorentz-broadened peaks, ...
• There is a highlighted demo that shows the issue in action. Preferably based on some reference calculations. Maybe two demos? Harmonic oscillator and Morse oscillator, for example?
  • Can the MolVibration/OH/3 demo be converted to such a highlighted demo?

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Implemented; only implemented a Lorentzian as functor; converted MolVibration/OH/3 to use this scheme with spectral density 1/E.

I am not quite sure yet about the usage of functors for spectral densities, which is why only a single Lorentzian was implemented. Needs some more playtesting to get a good feeling for what you might want to do.

Along the way, I am also not quite sure what to do with the terms that are not easy to calculate (time-dependent Lindblad, Lamb shift); altogether, using a Lindblad Liouvillian feels again awkward like what you do not want to use. Maybe I should try out the exact non-Markovian approach of Tannor etc.