Does Quantum Chaos Explain Quantum Statistical Mechanics?

TL;DR

This paper investigates whether quantum chaos underpins the emergence of thermal equilibrium in many-body quantum systems, demonstrating that classical chaos leads to thermalization of simple observables.

Contribution

It establishes a link between classical chaos and quantum thermalization, showing that simple observables reach thermal equilibrium in classically chaotic quantum systems.

Findings

Simple observables approach thermal averages in chaotic systems

Quantum chaos explains thermalization in many-body quantum systems

Thermalization occurs regardless of initial states in chaotic regimes

Abstract

If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langle\psi(t)|A_i|\psi(t)\rangle$, where $|\psi(t)\rangle$ is the system's state vector and $A_i$ is an experimentally accessible observable, should approach a constant value which is independent of the initial state, and equal to a thermal average of $A_i$ at an appropriate temperature. We show that this is the case for all simple observables whenever the system is classically chaotic.