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Séminaire de Physique Mathématique - EDP

Responsable : Laurent.Michel

  • Le 7 avril 2020 à 11:30
  • Salle de Conférences
    C. Fermanian
    Théorème d'Egorov sur les groupes de type Heisenberg
    Nous présenterons dans cet exposé des résultats récents obtenus en collaboration avec Véronique Fischer (University of Bath, UK) et visant à développer une analyse semi-classique sur les groupes de Lie. Nous discuterons un calcul pseudodifférentiel semi-classique sur ces groupes ainsi que les théorèmes de type Egorov et la notion de mesure semi-classique qui en découlent dans le cas des groupes de type Heisenberg.
  • Le 14 avril 2020 à 11:30
  • Salle de Conférences
    D. Häfner (Grenoble)

  • Le 21 avril 2020 à 11:30
  • Salle de Conférences
    C. Collot
    On the derivation of the homogeneous kinetic wave equation
    The kinetic wave equation arises in many physical situations: the description of small random surface waves, or out of equilibria dynamics for large quantum systems for example. In this talk we are interested in its derivation as an effective equation from the nonlinear Schrodinger equation (NLS) for the microscopic description of a system. More precisely, we will consider (NLS) in a weakly nonlinear regime on the torus in any dimension greater than two, and for highly oscillatory random Gaussian fields as initial data. A conjecture in statistical physics is that there exists a kinetic time scale on which, statistically, the Fourier modes evolve according to the kinetic wave equation. We prove this conjecture up to an arbitrarily small polynomial loss in a particular regime, and obtain a more restricted time scale in other regimes. The main difficulty, that I will comment on, is that one needs to identify the leading order statistically observable nonlinear effects. This means understanding correlation between Fourier modes, and relating randomness with stability and local well-posedness. The key idea of the analysis is the use of Feynman interaction diagrams to understand the solution as colliding linear waves. We use this framework to construct an approximate solution as a truncated series expansion, and use in addition random matrices tools to obtain its nonlinear stability using Bourgain spaces. This is joint work with P. Germain from Courant Institute, New York University.
  • Le 12 mai 2020 à 11:30
  • Salle de Conférences
    J. Faupin (Univ. Lorraine)

  • Le 19 mai 2020 à 11:30
  • Salle de Conférences
    A. Stingo (UC Davies)

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