Perturbative treatment of inter-site couplings in the local description of open quantum networks

TL;DR

This paper develops a perturbative method to improve the local approach for modeling open quantum networks with weak inter-site couplings, ensuring thermodynamic consistency and clarifying its validity.

Contribution

It introduces a systematic perturbation expansion to correct the local approach, addressing its limitations and validating its thermodynamic consistency.

Findings

Derived corrections to the local approach for weakly coupled sites.

Established the validity range of the perturbative corrections.

Confirmed the second law of thermodynamics in the corrected model.

Abstract

The problem of construction of a quantum master equation for a system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. Microscopic derivation of a quantum master equation requires a diagonalization of the Hamiltonian of the network, which can be a difficult task. When the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. Recently, some doubts were cast to the consistency of the local approach. We develop a systematic perturbation expansion to derive corrections to the local approach and establish its range of validity. Using this extension of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.