Temperature of a single chaotic eigenstate

TL;DR

This paper investigates how a single chaotic eigenstate in a finite bosonic system can exhibit thermalization, defining its temperature and analyzing the emergence of Bose-Einstein distribution through analytical and numerical methods.

Contribution

It introduces a method to define the temperature of a single eigenstate with chaotic structure, linking it to interaction strength and energy, and provides analytical and numerical insights.

Findings

Eigenstate temperature can be defined for chaotic states.

Bose-Einstein distribution emerges in single eigenstates.

Analytical expressions match numerical data.

Abstract

The onset of thermalization in a closed finite system of randomly interacting bosons, at the level of a single eigenstate, is discussed. The main interest is in the emergence of the Bose-Einstein distribution of single-particle occupation numbers, establishing a global and local criterion for thermalization. We show how to define the temperature of a given eigenstate, provided that it has a chaotic structure in the basis defined by single-particle states. The analytical expression for the eigenstate temperature as a function of the inter-particle interaction and energy is complemented by numerical data.