Open Systems' Density Matrix Properties in a Time Coarsened Formalism

TL;DR

This paper investigates the effects of time coarsening on open quantum systems, revealing how selective sampling influences equilibration, classicality emergence, and differences from traditional environment tracing methods.

Contribution

It introduces a non-uniform time-sampling approach dependent on bath properties and analyzes its impact on open system dynamics and classicality transition.

Findings

Time coarsening affects initial state independence of equilibration.

Deviations from long-term averages depend on environment size.

Time coarsening approach differs from environment tracing in open systems.

Abstract

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties (whether thermalized or not) of the bath. It is also applicable when an open microscopic sub-system is coupled to another {\it finite} system. By use of a time-periodic minimal coupling model between these two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett-Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method.