Limites de champ moyen bosoniques à température positive

2018/11/16 by Nicolas Rougerie, Rougerie, Nicolas
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1811.06755

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I present recent results in quantum statistical mechanics, obtained in joint works with Mathieu Lewin and Phan Thành Nam. We consider a certain mean-field limit of the grand-canonical ensemble for a Bose gas at positive temperature. In this limit, the reduced density matrices of the quantum theory converge to their analogues in classical field theory, given by a non-linear Gibbs measure. In particular, we deal with cases where the latter must be defined via a renormalization procedure. The corresponding renormalization at the level of the original quantum grand-canonical model, with non-commuting fields, is one of the important difficulties.

Citations

• A Perspective on Constructive Quantum Field Theory

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