Adapted projection operator technique for the treatment of initial correlations

TL;DR

This paper introduces a perturbative projection operator method that accurately models the dynamics of open quantum systems with arbitrary initial correlations, overcoming limitations of traditional approaches that assume uncorrelated initial states.

Contribution

The authors develop a family of adapted projection operators that handle general initial correlations, leading to a set of homogeneous differential equations for open-system dynamics.

Findings

Reproduces expected long-time behavior more accurately.

Applicable to any microscopic system-environment model.

Handles fully general initial correlations.

Abstract

The standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances, such as when the coupling between the system and the environment is weak or when the interaction starts at a distinguished time, the use of initially uncorrelated states is questionable if one wants to deal with general models, taking into account the mutual influence that the open-system and environmental evolutions perform on each other. Here, we introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Extending the standard technique based on projection operators that single out the relevant part of the global dynamics, we define a family of projections adapted to a convenient decomposition of the initial state, which involves a convex mixture of product operators with proper environmental states. This leads us to characterize the open-system dynamics via an uncoupled system of differential equations, which are homogeneous and whose number is limited by the dimensionality of the open system, for any kind of initial correlations. Our method is further illustrated by means of two cases study, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.