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Pré-publication, Document de travail

Fast rotating Bose-Einstein condensates in an asymmetric trap

Abstract : We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form defining the energy. This reduction allows us to simplify the energy on a Bargmann space and study the asymptotics of large rotational velocity. We characterize two regimes of velocity and anisotropy; in the first one where the behaviour is similar to the isotropic case, we construct an upper bound: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile. The second regime deals with very large velocities, a case in which we prove that the ground state does not display vortices in the bulk, with a 1D limiting problem. In that case, we show that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction but keeps a fixed profile given by a Gaussian in the other direction. The features of this second regime appear as new phenomena.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-00342278
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Soumis le : jeudi 27 novembre 2008 - 07:22:01
Dernière modification le : mardi 16 novembre 2021 - 04:59:37
Archivage à long terme le : : lundi 7 juin 2010 - 22:04:15

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  • HAL Id : hal-00342278, version 1
  • ARXIV : 0811.4714

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Amandine Aftalion, Xavier Blanc, Nicolas Lerner. Fast rotating Bose-Einstein condensates in an asymmetric trap. 2008. ⟨hal-00342278⟩

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