Séminaire: Problèmes Spectraux en Physique Mathématique


Année 2017-2018



Les séminaires auront lieu à l' Institut Henri Poincaré, habituellement en salle 314.
Le séminaire est financé par le GDR "Dynamique quantique" du CNRS.

Pour tout renseignement complémentaire, veuillez contacter les organisateurs, Hakim Boumaza, Mathieu Lewin ou Stéphane Nonnenmacher.

Prochain séminaire le lundi 16 octobre 2017 en salle 314 (3e étage)
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 11h15 - 12h15 Jimmy Lamboley (Paris-6)
About optimal shapes for the Dirichlet-Laplace operator

Abstract:

We are interested in optimal estimates of the eigenvalues (or functions of eigenvalues) of the Laplace operator with Dirichlet boundary conditions, involving geometrical informations of the considered domains. We will briefly review some well-known results on this topic, and then focus on new existence and regularity results for problems involving the perimeter of the domain. We will conclude with some remarks, results, and open problems when domains are assumed to be convex.

Déjeuner
14h - 15h Nikhil Savale (Cologne)
A Gutzwiller type trace formula for the magnetic Dirac operator

Abstract:
For manifolds including metric-contact manifolds with non-resonant Reeb flow, we prove a Gutzwiller type trace formula for the associated magnetic Dirac operator involving contributions from Reeb orbits on the base. The method combines the use of almost analytic continuations and local index theory. The construction of appropriate microlocal weight/trapping functions then allows extension of the formula to large time. As an application, we prove a semiclassical limit formula for the eta invariant of the Dirac operator.
15h15 - 16h15 Sébastien Breteaux (Metz)
Quantum Mean Field Asymptotics and Multiscale Analysis

Abstract:
In this work, we study how multiscale analysis and quantum mean field asymptotics can be brought together. In particular we study when a sequence of one-particle density matrices has a limit with two components : one classical and one quantum. The introduction of “separating quantization for a family” provides a simple criterion to check when those two types of limit are well separated. We give examples of explicit computations of such limits, and how to check that the separating assumption is satisfied.
This is joint work with Z.Ammari and F.Nier.


Prochaines dates prévues:

13 novembre 2017: Thomas Letendre, Alain Joye, Yan Pautrat
18 décembre 2017: Stefano Olla, Laurent Michel, Vincent Bruneau
15 janvier 2018

Informations pratiques: Plan d'accès à l'IHP.

Historique du séminaire:

Année 2016-2017
Année 2015-2016
Année 2014-2015
Année 2013-2014
Année 2012-2013
Année 2011-2012
Année 2010-2011
Année 2009-2010
Année 2008-2009
Année 2007-2008
Année 2006-2007
Année 2005-2006

Dernière mise à jour: 27 septembre 2017
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