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Mathieu Lewin
Derivation of Hartree’s theory for mean-field Bose gases
(Dérivation de la théorie de Hartree pour des gaz de bosons dans le régime de champ moyen)
Journées équations aux dérivées partielles (2013), Exp. No. 7, 21 p., doi: 10.5802/jedp.103
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Class. Math.: 35Q40, 81Q99
Mots clés: Hartree theory, mean-field limit, Bose-Einstein condensation, quantum de Finetti theorem

Résumé - Abstract

Dans cet article, nous présentons des résultats obtenus avec Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty et Jan Philip Solovej. Nous considérons un système de $N$ bosons qui interagissent avec un potentiel d’intensité $1/N$ (on parle de régime de champ moyen). Dans la limite où $N\rightarrow \infty $, nous montrons que le premier ordre du développement des valeurs propres du Hamiltonien à $N$ corps est donné par la théorie non linéaire de Hartree, alors que l’ordre suivant est donné par l’opérateur de Bogoliubov. Nous discutons également en détails du phénomène de condensation de Bose-Einstein dans de tels systèmes.

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