Equilibration times in closed quantum many-body systems

TL;DR

This paper explores the timescales over which closed quantum many-body systems reach equilibrium, connecting theoretical insights with recent experimental developments and summarizing rigorous results on equilibration times.

Contribution

It provides a comprehensive overview of equilibration times in closed quantum systems, combining heuristic understanding with a review of rigorous theoretical findings.

Findings

Connection between equilibration times and experimental quantum simulators

Heuristic insights into the factors influencing equilibration

Summary of rigorous mathematical results on equilibration times

Abstract

For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter, we discuss the problem of equilibration and specifically provide insights into how long it takes to reach equilibrium in closed quantum systems. We first briefly discuss the connection of this problem with recent experiments and forthcoming quantum simulators. Then we provide a comprehensive discussion of equilibration from a heuristic point of view, with a focus on providing an intuitive understanding and connecting the problem with general properties of interacting many-body systems. Finally, we provide a concise review of the rigorous results on equilibration times that are known in the literature.