The interacting 2D Bose gas and nonlinear Gibbs measures

Mathieu Lewin (1) , Phan Thành Nam (2) , Nicolas Rougerie (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München
3 LPM2C - Laboratoire de physique et modélisation des milieux condensés

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.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]; Physique Numérique [physics.comp-ph]

Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie. The interacting 2D Bose gas and nonlinear Gibbs measures . Gibbs measures for nonlinear dispersive equations, Giuseppe Genovese, Benjamin Schlein and Vedran Sohinger, Apr 2018, Oberwolfach (Germany), Germany. p. 1088, ⟨10.4171/OWR/2018/18⟩. ⟨hal-01784153⟩