Exact homogeneous master equation for open quantum systems incorporating initial correlations

TL;DR

This paper derives an exact homogeneous master equation for open quantum systems that includes initial correlations, revealing how these correlations influence fluctuation dynamics and extending the fluctuation-dissipation theorem.

Contribution

It provides the first explicit derivation of a homogeneous master equation incorporating initial correlations for a broad class of quantum systems.

Findings

Initial correlations can be fully embedded into fluctuation dynamics.

The derived master equation is homogeneous for both bosonic and fermionic systems.

A generalized fluctuation-dissipation theorem including initial correlations is established.

Abstract

We show that the exact master equation incorporating initial correlations for open quantum systems, within the Nakajima-Zwanzig operator-projection method, is a homegenous master equation for the reduced density matrix. We also derive explicitly the exact master equation for a large class of bosonic and fermionic open quantum systems incorporating initial correlations, the resulting master equation is homogenous. We find that the effects of the initial correlations can be fully embedded into the fluctuation dynamics through the exact homogenous master equation. Also a generalized nonequilibrium fluctuation-dissipation theorem incorporating the initial correlations is obtained.