Dynamical typicality approach to eigenstate thermalization

TL;DR

This paper demonstrates that in isolated quantum systems, most initial states with a fixed non-equilibrium expectation value thermalize if and only if the observable satisfies the weak eigenstate thermalization hypothesis, using a dynamical typicality approach.

Contribution

It introduces a dynamical typicality framework to connect initial state properties with the weak eigenstate thermalization hypothesis for thermalization.

Findings

Most initial states with a fixed expectation value thermalize under wETH.

Thermalization occurs when eigenstates have similar expectation values of the observable.

The approach links initial state sets to eigenstate properties via dynamical typicality.

Abstract

We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit the same, arbitrary but fixed non-equilibrium expectation value for some given observable $A$. On condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if $A$ satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of $A$ spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of $A$.