Bose Gases at Positive Temperature and Non-Linear Gibbs Measures

TL;DR

This paper explores the relationship between positive temperature equilibrium states of large bosonic systems and classical Gibbs measures, highlighting recent advances and comparing with distinguishable particles to deepen understanding of quantum statistical mechanics.

Contribution

It establishes a connection between bosonic grand-canonical states and classical Gibbs measures derived from mean-field energy functionals, advancing the theoretical framework.

Findings

Link between bosonic states and classical Gibbs measures clarified

Comparison with boltzons highlights unique quantum effects

Recent results on equilibrium states summarized

Abstract

We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal states and the (semi-) classical Gibbs measures on one-body quantum states built using the corresponding mean-field energy functionals. An illustrative comparison with the case of "distinguishable" particles (boltzons) is provided.