This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is
among the most fundamental problems in statistical physics. Recent theoretical studies have …

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ
spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state …

Over the past decade, there has been remarkable progress in our understanding of
equilibration, thermalization and prethermalization, due in large part to experimental …

The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe
observables in isolated integrable quantum systems after equilibration. Since then, the GGE …

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 …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

Entanglement and entropy are key concepts standing at the foundations of quantum and
statistical mechanics. Recently, the study of quantum quenches revealed that these …

This review is devoted to the problem of thermalization in a small isolated conglomerate of
interacting constituents. A variety of physically important systems of intensive current interest …