The temperature of a single chaotic eigenstate

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.