A perturbative method for nonequilibrium steady state of open quantum systems

TL;DR

This paper introduces a perturbative approach to accurately compute the nonequilibrium steady state of open quantum systems weakly coupled to reservoirs, improving computational efficiency for larger systems.

Contribution

The authors develop a perturbative method based on decomposing the Redfield QME, enabling first-order accurate NESS calculations with enhanced numerical scalability.

Findings

Method yields exact first-order NESS in system-reservoir coupling

Applicable to larger systems than direct Redfield QME solutions

Derived analytical NESS for noninteracting fermion systems

Abstract

We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part $\mathcal{R}$. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to $\mathcal{R}$ to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.