Reduced density matrix for nonequilibrium steady states: A modified Redfield solution approach

TL;DR

This paper introduces a modified Redfield approach to accurately compute the reduced density matrix in nonequilibrium steady states, validated against exact Green's function results and compared with other quantum master equations.

Contribution

The authors develop a second-order accurate method for nonequilibrium steady states using an analytic continuation scheme based on a Redfield-like quantum master equation.

Findings

The method accurately reproduces the RDM for a quantum harmonic oscillator.

It is validated against exact nonequilibrium Green's function results.

The scheme shows advantages over traditional Lindblad and Redfield QMEs.

Abstract

We describe a method to obtain the reduced density matrix (RDM) correct up to second order in system-bath coupling in \emph{nonequilibrium} steady state situations. The RDM is obtained via a scheme based on analytic continuation, using the time-local Redfield-like quantum master equation, which was earlier used by the same authors [J. Chem. Phys. \textbf{136}, 194110 (2012)] to obtain the correct thermal equilibrium description. This nonequilibrium modified Redfield solution is then corroborated with the exact RDM obtained via the nonequilibrium Green's function technique for the quantum harmonic oscillator. Lastly, the scheme is compared to different quantum master equations (QMEs), namely the time-local Redfield-like and the Lindblad-like QMEs, in order to illustrate the differences between each of these approaches.