#158 Helper functionality to setup standard Lindblad relaxation

[Ulf Lorenz]

Covered by [#155] and [#230]

What and Why

We currently have all the required functionality to setup a Lindblad problem: Lots of operators and a LindbladLiouvillian. However, to actually setup a relaxation, we still need to setup the Lindblad relaxation operators.

Usually, this is done in the energy representation, where we set up something like a ladder operator with entries depending on some simple heuristics (e.g., Fermi's golden rule). This currently requires a lot of manual work and must be a lot simpler.

Acceptance criteria

• Implement a helper function to easily set up a Lindblad relaxation term based on Fermi's golden rule.
  See MolVibration/OH/3 demo and the Matlab code for control.relax.model == 'fermi'
• upgrade the demo MolVibration/OH/3 to use this new code

State after first try

I simply could not set up a Lindblad Liouvillian that implements a rate equation. Apparently, going through network references, basically, Lindblad Liouvillians are usually set up for toy systems (qubits or harmonic oscillators with the destruction operator as jump operator). Playing around with some examples, it seems that these give good results only because every row and column in the jump operator matrix has a single occupation. If I relax this requirement, I get strange results, for example a diagonal density operator acquires coherences.

Also, the Matlab code does not set up the jump operator, but directly sets up the master equation in the dual space. This is maybe the way to go, but requires some prerequisites, [#229]. The current branch is still available, if there are useful things in it.