Relaxation to equilibrium of expectation values in macroscopic quantum systems

TL;DR

This paper provides a quantum mechanical explanation and numerical verification of how macroscopic nonintegrable quantum systems relax to equilibrium after external perturbations, with expectation values approaching microcanonical averages.

Contribution

It offers a quantitative explanation for relaxation to equilibrium in macroscopic quantum systems, supported by numerical verification for nonintegrable cases.

Findings

Expectation values approach microcanonical averages after perturbation

Numerical verification confirms theoretical predictions

Relaxation occurs in nonintegrable macroscopic systems

Abstract

A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally perturbed during a finite time, and then isolated for a sufficiently long time. We show a quantitative explanation that the initial microcanonical state typically reaches to a state whose expectation values are well-approximated by the average over another microcanonical ensemble.