Perturbative Analysis of Nonequilibrium Steady States in Quantum Systems

TL;DR

This paper develops a perturbative method to analyze nonequilibrium steady states in quantum systems coupled to heat baths, providing explicit density matrix representations and confirming the Kubo formula's validity.

Contribution

It introduces a time-independent perturbative approach for NESS in quantum systems, with explicit density matrix forms and energy current calculations.

Findings

Explicit density matrix representation for symmetric, weakly nonequilibrium cases

Validation of the Kubo formula in the studied regime

Analytical expressions for energy current

Abstract

We study the nonequilibrium steady state (NESS) in a quantum system in contact with two heat baths at different temperatures. We use a time-independent perturbative expansion with respect to the coupling with the two heat baths to obtain the density matrix for the NESS. In particular, we show an explicit representation of the density matrix for the reflection symmetric and weakly nonequilibrium case. We also calculate the expectation value of the energy current and show that the Kubo formula holds in this case.