Fast rotating Bose-Einstein condensates and Bargmann transform

Blanc, Xavier

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 5, 18 p.

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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