Study of non-equilibrium Green's functions beyond Born approximation in open quantum systems

TL;DR

This paper develops a systematic method to compute non-equilibrium Green's functions in open quantum systems beyond the Born approximation, accurately capturing system-bath correlations and steady-state energy currents.

Contribution

It introduces a correction to Green's functions that accounts for finite system-bath correlations, improving accuracy in weak coupling regimes.

Findings

Correctly reproduces Kadanoff-Baym equations for Green's functions.

Provides accurate long-time results up to first non-zero order of coupling.

Derives expressions for non-equilibrium steady-state energy currents.

Abstract

We provide a systematic approach to compute different kinds of non-equilibrium Green's functions for open quantum systems which are essentially two-point correlation functions in time. We reveal that the definition of Green's functions based on the Born approximation does not provide the correct results in the leading order of the system-bath coupling. We next provide a systematic correction term in Green's functions by going beyond the Born approximation and incorporating a finite correlation between the system and the bath. We primarily focus on two paradigmatic models of open quantum systems, namely, the dissipative Caldeira-Leggett model and the dissipative spin-boson model. We show that the inclusion of such a correction correctly reproduces the Kadanoff-Baym type equation for the so-called lesser or greater components of the Green's functions and provides the correct long-time result up to the first non-zero order of the system-bath coupling, satisfying the detailed balance condition in thermal equilibrium. We further extend our study to a system coupled to multiple reservoirs simultaneously that are maintained at different temperatures and obtain expressions for non-equilibrium steady-state energy current, once again correct up to the first non-zero order of the system-bath coupling.