Equation of Motion for Open Quantum Systems incorporating Memory and Initial Correlations

TL;DR

This paper derives a generalized equation of motion for open quantum systems that includes memory effects and initial correlations, extending traditional semi-group dynamics and demonstrating long-term stationarity.

Contribution

It introduces an effective Liouville operator framework that captures memory and initial correlations within the system's dynamics, generalizing existing models.

Findings

The effective Liouville operator can have a non-degenerate zero mode.

Open systems tend to a stationary state independent of initial conditions.

The framework accommodates frequency-dependent effects and initial correlations.

Abstract

An equation of motion for open quantum systems incorporating memory effects and initial correlations with the environment is presented in terms of an effective Liouville operator that solely acts on states of the system. The environment can induce memory effects via the frequency dependence of the effective Liouville and initial correlations can be mapped to a shifted frequency dependent initial state within the system. The equation of motion generalizes the well known semi-group dynamic equations. In generic systems the effective Liouville has a non-degenerate zero mode. By probability conservation one can demonstrate that a generic open system reaches, in the long time limit, a stationary state, which is independent of any initial condition.