Thermalizing two identical particles

TL;DR

This paper explores how identical bosons can exhibit Bose-Einstein statistics and correlations through indirect interactions with a shared environment, emphasizing the roles of reversible and irreversible processes in thermalization.

Contribution

It provides a theoretical framework explaining how non-interacting bosons thermalize and develop correlations via joint measurement interactions and competing processes.

Findings

Correlations depend on initial orthogonal states.

Thermalization involves reversible and irreversible processes.

Indistinguishability leads to Bose-Einstein statistics without direct interaction.

Abstract

How do indistinguishable identical bosons manage to obey Bose-Einstein statistics---and hence be correlated---even when they do not interact with each other? Part of the answer is that the bosons have to interact indirectly with each other by interacting with the same environment. A joint measurement interaction provides a good example. Thermalization occurs whenever there are two competing processes, one diagonal in the energy basis (namely, reversible Hamiltonian evolution), the other irreversible and diagonal in a complementary basis (for example, a measurement in a spatially localized basis). Correlations arise only from initial states in which the bosons start in different (orthogonal) states.