Large-scale limits of interacting particle systems

Collection Large-scale limits of interacting particle systems

Organizer(s) Mitia Duerinckx, Sergio Simonella, and Raphael Winter
Date(s) 10/4/21 - 10/8/21
linked URL'21.html
00:00:00 / 00:00:00
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Bose gases at positive temperature and non-linear Gibbs measures

By 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

Information about the video

  • Date of recording 10/8/21
  • Date of publication 10/13/21
  • Institution IHES
  • Language English
  • Director(s) Mandarine Audiovisuel
  • Format MP4

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