Influence of initial correlations on evolution over time of an open quantum system

TL;DR

This paper introduces a new method to incorporate initial system-bath correlations into the dynamics of open quantum systems, using homogeneous generalized master equations that are valid across all timescales.

Contribution

It develops an exact conversion of inhomogeneous GMEs into homogeneous GMEs that include initial correlations, applicable in the second order approximation and for realistic initial states.

Findings

Initial correlations affect the phase of the system's correlation function.

The derived HGMEs are local in time and valid at all timescales.

The method is demonstrated on a quantum oscillator interacting with a Boson field.

Abstract

A novel approach to accounting for the influence of initial system-bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima-Zwanzig inhomogeneous generalized master equations (GMEs) for a system's reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system-bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at $t=t_0$) system+bath state (for a system reduced statistical operator an external force at $t>t_0$ is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system's correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system-bath correlations.