A master equation incorporating the system-environment correlations present in the joint equilibrium state

TL;DR

This paper introduces a second-order master equation that incorporates initial system-environment correlations, crucial for accurately modeling quantum system dynamics after preparing the initial state from a joint thermal equilibrium.

Contribution

It presents a novel master equation formulation that explicitly includes initial correlations, extending traditional models that neglect such correlations.

Findings

Initial correlations significantly affect system dynamics.

The new master equation accurately predicts behavior in spin-boson and spin environments.

Neglecting initial correlations can lead to inaccurate results.

Abstract

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.