Séminaire: Problèmes Spectraux en Physique Mathématique

Année 2023-2024

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

Prochain séminaire le lundi 13 mai 2024 après-midi à l'Institut Henri Poincaré, en salle Pierre Grisvard (3e étage, ex-314)

14h - 15h Frédéric Klopp (Sorbonne Univ.)

The ground state of a system of interacting fermions in a random field: localization, entanglement entropy, ...

Transport in disordered solids is a phenomenon involving many actors. The motion of a single quantum particle in such a solid is described by a random Hamiltonian. Transport involves many interacting particles, usually, a small fraction of the particles present in the material. One striking phenomenon observed and proved in disordered materials is localization: disorder can prevent transport! While this is quite well understood at the level of a single particle, it is much less clear what happens in the case of many interacting particles. Physicist proposed a number of tools (exponential decay of finite particle density matrices, entanglement entropy, etc) to discriminate between transport and localization. Unfortunately, these quantities are very difficult to control mathematically for "real life" models. We'll present a toy model where one can actually get a control on various of these quantities at least for the ground state of the system.

The talk is based on the PhD theses of and joint work with N. Veniaminov and V. Ognov.

 15h15 - 16h15 Christof Sparber (Univ. of Illinois at Chicago) Nonlinear bound states with prescribed angular momentum

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of a non-radially symmetric spatial profile which in itself is obtained via a doubly constrained energy minimization. One of the two constraints imposed is the total mass, while the other is given by the expectation value of the angular momentum around the z-axis. Our approach also allows for a new description of the set of minimizers subject to only a single mass constraint.

This is joint work with I. Nenciu and X. Shen.

Prochaines séances :

17 juin 2024: Pablo Miranda, Mi-Song Dupuy

Historique du séminaire:

Année 2023-2024
Année 2022-2023
Année 2021-2022
Année 2020-2021
Année 2019-2020
Année 2018-2019
Année 2017-2018
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: 12 janvier 2024
Page maintenue par Stéphane Nonnenmacher