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Temperature of a single chaotic eigenstate
Fausto Borgonovi1,2, Francesco Mattiotti1, Felix M Izrailev3,4
1Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia, Italy.
Abstract:
The onset of thermalization in a closed system of randomly interacting bosons at the level of a single eigenstate is discussed. We focus on the emergence of Bose-Einstein distribution of single-particle occupation numbers, and we give a local criterion for thermalization dependent on the eigenstate energy. We show how to define the temperature of an eigenstate, provided that it has a chaotic structure in the basis defined by the single-particle states. The analytical expression for the eigenstate temperature as a function of both interparticle interaction and energy is complemented by numerical data.
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