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Séminaire Équations aux dérivées partielles (Polytechnique)

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Xavier Blanc
Fast rotating Bose-Einstein condensates and Bargmann transform
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Exp. No. 5, 18 p.
Article PDF | Reviews MR 2276071

Résumé - Abstract

When a Bose-Einstein condensate (BEC) is rotated sufficiently fast, it nucleates vortices. The system is only stable if the rotational velocity $\Omega $ is lower than a critical value $\Omega _c$. Experiments show that as $\Omega $ approaches $\Omega _c$, the condensate nucleates more and more vortices, which become periodically arranged. We present here a mathematical study of this limit. Using Bargmann transform and an analogy with semi-classical analysis in second quantization, we prove that the system necessarily has an infinite number of vortices and provide an ansatz for the solution. This summarizes two joint works, with A. Aftalion (LJLL, Univ. Paris 6) and J. Dalibard (LKB, Ecole Normale Supérieure), on the one hand, and with A. Aftalion and F. Nier (IRMAR, Univ. Rennes I) on the other hand.


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