Large-scale limits of interacting particle systems

Collection Large-scale limits of interacting particle systems

Organisateur(s) Mitia Duerinckx, Sergio Simonella, and Raphael Winter
Date(s) 04/10/2021 - 08/10/2021
URL associée http://homepages.ulb.ac.be/~mduerinc/workshop'21.html
00:00:00 / 00:00:00
14 16

Bose gases at positive temperature and non-linear Gibbs measures

De Nicolas Rougerie

I shall discuss a certain mean-field limit for the positive temperature equilibria (Gibbs states) of the interacting Bose gas. This serves as a toy model for the understanding of the phase transition towards a Bose-Einstein condensate when the temperature is lowered. The limit model we rigorously derive is a classical field theory, based on a certain non-linear Gibbs measure. The latter is a natural invariant of the non-linear Schrödinger equation approximating the dynamics of the Bose gas. It is also the basic ingredient of the Euclidean approach to constructive quantum field theory, as well as the large-time asymptote for the stochastic non-linear heat equation. A difficulty is that this non-linear Gibbs measure lives on low regularity distributional spaces, so that the non-linearity has to be understood in a renormalized sense. I shall put emphasis on the control of the renormalization procedure at the level of the quantum many-body model.

Based on joint work with Mathieu Lewin and Phan Thành Nam

Informations sur la vidéo

  • Date de captation 08/10/2021
  • Date de publication 13/10/2021
  • Institut IHES
  • Langue Anglais
  • Réalisateur(s) Mandarine Audiovisuel
  • Format MP4

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow




Inscrivez-vous

  • Mettez des vidéos en favori
  • Ajoutez des vidéos à regarder plus tard &
    conservez votre historique de consultation
  • Commentez avec la communauté
    scientifique
  • Recevez des notifications de mise à jour
    de vos sujets favoris
Donner son avis