Quantifying the influence of the initial state on the dynamics of an open quantum system

TL;DR

This paper investigates how the initial state of an open quantum system can influence its long-term behavior, proposing a measure to quantify this effect and applying it to the spin-boson model.

Contribution

It introduces a new measure to quantify initial state influence on open quantum system dynamics and derives conditions for unique asymptotic states.

Findings

Identifies three distinct long-time behaviors in the spin-boson model.

Proposes criteria to distinguish these behaviors based on the measure.

Shows that initial states can affect the asymptotic state under certain conditions.

Abstract

A small system in contact with a macroscopic environment usually approaches an asymptotic state, determined only by some macroscopic properties of the environment such as the temperature or the chemical potential. In the long-time limit, the state of the small system is thus expected to be independent of its initial state. In some situations, however, the asymptotic state of the system is influenced by its initial state and some information about the initial state is kept for all times. Motivated by this finding, we propose a measure to quantify the influence of the initial state of an open system on its dynamics. Using this measure we derive conditions under which the asymptotic state exists and is unique. We demonstrate our concepts for the dynamics of the spin-boson model, identify three qualitatively different long-time behaviors, and discuss how they can be distinguished based on the proposed measure.