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Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime

le 14 octobre 2015

11h - Groupe de travail "Applications des Mathématiques"

ENS Rennes Bâtiment Sauvy, Salle 5 (rdc)

Séminaire de Loïc Le Treust (Université de Rennes 1) au groupe de travail "Applications des mathématiques"

Groupe de travail


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Résumé :
We study the problem of dimension reduction for the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyze two combined singular limits: a semi-classical limit in the transport direction and the strong partial confinement limit in the transversal direction. We prove that both limits commute together and we provide convergence rates. The by-products of this work are approximated models in reduced dimension for the GPE, with a priori estimates of the approximation errors.
Work in collaboration with Weizhu BAO and Florian MÉHATS.

Recherche - Valorisation
Thibaut Deheuvels et Nicolas Crouseilles

Mise à jour le 11 mars 2016