Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

TL;DR

This paper introduces a modified Redfield approach that accurately predicts the steady state of quantum systems up to second order, matching exact results without higher-order tensors, and simplifies numerical computations.

Contribution

The authors develop an analytic continuation scheme for the Redfield solution that achieves second-order accuracy and reduces computational complexity without requiring higher-order relaxation tensors.

Findings

Accurately predicts the generalized Gibbs state up to second order.

Shows good agreement with nonequilibrium Green's function results at low temperatures.

Significantly reduces numerical complexity for large systems.

Abstract

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correct coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus allowing to study efficiently large-sized \emph{system} Hilbert spaces.