Including noise terms in the symbolic derivation

[DHuybrechts]

Hello, I was having a look at your interesting paper and code and I was wondering if it would be difficult to include the noise terms of the quantum Langevin equations into the derivation? It would be interesting since the inclusion of these terms in the (stochastic) evolution have been shown to yield good results for the description of the dynamics/ steady states of several models.

It seems to me that all building blocks should be present here, i.e. the symbolic derivation, transformation to an ODESystem and then solving it with an ODEProblem. If the symbolic derivation could output a new ODESystem describing the stochastic noise contribution to the dynamics then I suppose this ODESystem can be used, in addition to the already existing functionality for the deterministic ODEProblem, to solve an according SDESystem.

I am checking with you if you believe this approach would be feasible, as I am not yet very familiar with the inner workings of the package. Any remarks and suggestions would be much appreciated, as well as possibly pointing me in the direction of the functions I would need to take a closer look at to implement this.

Thanks in advance!

[ChristophHotter]

Hi @DHuybrechts
Yes, that's correct, all building blocks are there and it should be straightforward to include the noise.
@Nico0oblr is currently working on including noise from measurement back-action, once this is implemented it should be easy to adapt the code for the noise of the quantum Langevin equation. Maybe you could have a look at his measurement_backaction branch.

In the following papers they also include noise for measurement back-action, they show some code in the appendix:
https://arxiv.org/pdf/2306.00868.pdf
https://arxiv.org/abs/2211.13068

Let me know if you need more information.

[DHuybrechts]

Thank you very much for this information @ChristophHotter! I will have a look at the suggest branch. From a very quick look at the papers I do indeed believe this is exactly what I was searching for, thank you for pointing me in this direction.