Chaos and thermalization in small quantum systems

TL;DR

This paper discusses how small quantum systems can exhibit thermalization through chaos and the eigenstate thermalization hypothesis, bridging microscopic quantum behavior with macroscopic thermodynamic phenomena.

Contribution

It reviews recent theoretical and experimental advances demonstrating quantum thermalization and the role of entanglement in small quantum systems.

Findings

Quantum systems can thermalize despite formal differences from classical systems.

Experimental evidence shows small lattice systems relax to thermal states.

Entanglement entropy measurements confirm local thermalization.

Abstract

Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical ensemble, quantum systems formally can not. Recent theoretical breakthroughs and, in particular, the eigenstate thermalization hypothesis (ETH) however indicate that quantum systems can also thermalize. In fact ETH provided us with a framework connecting microscopic models and macroscopic phenomena, based on the notion of highly entangled quantum states. Such thermalization was beautifully demonstrated experimentally by A. Kaufman et. al. who studied relaxation dynamics of a small lattice system of interacting bosonic particles. By directly measuring the entanglement entropy of subsystems, as well as other observables, they showed that after the initial transient time the system locally relaxes to a thermal ensemble while globally maintaining a zero-entropy pure state.