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amartyabose / QuantumDynamics.jl

quantum dynamics simulation environment
MIT License
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Variational MPO approach for finding NESS #32

Open 4psireal2 opened 4 months ago

4psireal2 commented 4 months ago

Would there soon be an implementation of Variational MPO approach for finding NESS? See ref

amartyabose commented 4 months ago

This would be good to put in. However I don't have the time to immediately work on this. Would you be willing to contribute? I can help you out.

4psireal2 commented 3 months ago

I'd be! However, I've encountered great difficulties with finding NESS for my system of interest using this approach. I'm afraid that this approach is not numerically stable... I'll share my experience more and perhaps contribute once I get better convincing results!

4psireal2 commented 3 months ago

Also what's your ansatz for the density matrix in the Lindblad master equation?

amartyabose commented 3 months ago

I'd be! However, I've encountered great difficulties with finding NESS for my system of interest using this approach. I'm afraid that this approach is not numerically stable... I'll share my experience more and perhaps contribute once I get better convincing results!

Hmmm... By the way, a naive question: how are you defining steady state if these open quantum systems? Are you talking about the equilibrium reduced density matrix?

amartyabose commented 3 months ago

Also what's your ansatz for the density matrix in the Lindblad master equation?

In the GQME module? It's represented just as a matrix. See here: GQME documentation

4psireal2 commented 3 months ago

So I'm interested in non-equilibrium steady state (NESS) . Given dρ/dt = Lρ, steady state is a fixed point of the evolution dρ_s/dt = 0 and hence, ρ_s is a zero eigenvector of L. I hope that answers your question!

I see. I was thinking in a many-body setup, where the state is represented with a tensor network.