Stationary states of weak coupling limit type Markov generators and quantum transport models

TL;DR

This paper characterizes stationary states of certain Markov generators in quantum transport, revealing their structure and applying results to a modified quantum transport model using generalized operators.

Contribution

It proves the structure of stationary states for weak coupling limit Markov generators and applies this to analyze a modified quantum transport model.

Findings

Stationary states decompose into interaction-free and orthogonal components.

Detailed structure of the modified AKV quantum transport model is described.

Results utilize generalized annihilation and creation operators.

Abstract

We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva, Kozyrev and Volovich (modified AKV's model) studied first in Ref.\cite{gggq}, in terms of generalized annihilation and creation operators.