Marcos Rigol

TL;DR: It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.

TL;DR: The eigenstate thermalization hypothesis (ETH) as discussed by the authors is a natural extension of quantum chaos and random matrix theory (RMT) that allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath.

TL;DR: The relaxation hypothesis is confirmed through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice, and a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation.

TL;DR: The eigenstate thermalization hypothesis (ETH) as mentioned in this paper is a natural extension of quantum chaos and random matrix theory (RMT) and it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath.

TL;DR: The physics of one-dimensional interacting bosonic systems is reviewed in this paper, where the effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations.