Applied Analysis Seminar Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics

I will discuss joint work with Mathieu Lewin and Nicolas Rougerie on the rigorous derivation of the classical nonlinear Gibbs measures in three spatial dimensions from many-body bosonic systems in thermal equilibrium. The nonlinear Gibbs measures thus describe the behavior of infinite Bose gases close to the Bose-Einstein phase transition. The proof is based on a novel method to control quantum variances, which enables the desired Wick renormalization of the semiclassical limit.