Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

TL;DR

This paper reviews recent theoretical advances in understanding how closed quantum many-body systems naturally evolve towards statistical mechanics behavior, focusing on equilibration, thermalisation, and related phenomena.

Contribution

It provides a unified, rigorous overview of key concepts and results explaining emergent statistical mechanics in closed quantum systems, highlighting new theoretical insights.

Findings

Eigenstate thermalisation hypothesis supported by recent proofs

Conditions under which quantum systems equilibrate or fail to thermalise

Role of entanglement and Lieb-Robinson bounds in thermalisation processes

Abstract

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.