Derivation of the Redfield quantum master equation and corrections to it by the Bogoliubov method

TL;DR

This paper presents an alternative derivation of the Redfield quantum master equation using the Bogoliubov method, including higher-order corrections, and emphasizes the role of initial correlations in open quantum systems.

Contribution

It introduces a novel derivation approach for the Redfield equation and provides simpler expressions for higher-order corrections considering initial correlations.

Findings

Redfield equation derived without modifications for initially correlated states

Higher-order correction expressions are simplified compared to previous methods

Initial correlations do not alter the form of the Redfield equation

Abstract

Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum systems, as well as higher-order corrections to it. This derivation naturally considers initially correlated system-reservoir states arising from the previous system-reservoir dynamics. It turns out that the Redfield equation does not require any modifications in this case. The expressions of higher-order corrections are simpler than those obtained by other methods.