On the time scales in the approach to equilibrium of macroscopic quantum systems

TL;DR

This paper presents two theorems about the time evolution of isolated quantum systems, highlighting conditions for both extremely long and short relaxation times in reaching equilibrium.

Contribution

It introduces two theorems that clarify the possible time scales for a quantum system to approach equilibrium, addressing both slow and fast relaxation scenarios.

Findings

Existence of pathological cases with very long relaxation times

Existence of equilibrium subspaces with universally short relaxation times

Abstract

We prove two theorems concerning the time evolution in general isolated quantum systems. The theorems are relevant to the issue of the time scale in the approach to equilibrium. The first theorem shows that there can be pathological situations in which the relaxation takes an extraordinarily long time, while the second theorem shows that one can always choose an equilibrium subspace the relaxation to which requires only a short time for any initial state.