The interacting 2D Bose gas and nonlinear Gibbs measures

TL;DR

This paper establishes a rigorous link between quantum and classical fields for high-temperature 2D Bose gases by showing the grand-canonical quantum Gibbs state converges to a nonlinear Gibbs measure in a mean-field regime.

Contribution

It provides a new theorem connecting quantum Gibbs states to nonlinear classical Gibbs measures for 2D Bose gases at high temperature.

Findings

Quantum Gibbs state reduces to nonlinear Gibbs measure in mean-field regime

Establishes a rigorous connection between quantum and classical fields

Applicable to high-temperature 2D Bose gases

Abstract

We announce a new theorem bearing on high-temperature 2D Bose gases. In a certain mean-field-like regime, the grand-canonical quantum Gibbs state reduces to a nonlinear Gibbs measure constructed from a renormalized mean-field energy functional. This establishes a rigorous connection between quantum fields and (singular) classical fields in the regime of interest.