Bose Gases at Positive Temperature and Non-Linear Gibbs Measures

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.

Proceedings of the 18th ICMP, Santiago de Chile, July 2015

References in corpus (3)

• Mean-field limit of Bose systems: rigorous results
• Long time dynamics for the one dimensional non linear Schrödinger equation
• Invariant measure for the Schrödinger equation on the real line

Cited by in corpus (3)

• Some contributions to many-body quantum mathematics
• Semi-classical limit of large fermionic systems at positive temperature
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger