Vortices in a 2d rotating Bose–Einstein condensate

Radu Ignat; Vincent Millot

doi:10.1016/j.crma.2005.03.015

Partial Differential Equations

Vortices in a 2d rotating Bose–Einstein condensate

Presented by: Haïm Brezis

Radu Ignat ¹; Vincent Millot ¹

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 8, pp. 571-576.

Abstract
Résumé

We investigate the physical model for a two dimensional rotating Bose–Einstein condensate. We minimize a Gross–Pitaevskii functional defined in $R^{2}$ under the unit mass constraint. We estimate the critical rotational speeds $Ω_{d}$ for having d vortices in the condensate and we determine the location of the vortices. This relies on an asymptotic expansion of the energy.

Nous étudions le modèle physique pour un condensat de Bose–Einstein bidimensionnel en rotation. Nous minimisons une fonctionnelle de Gross–Pitaevskii définie sur $R^{2}$ sous contrainte de masse un. Nous estimons les vitesses critiques $Ω_{d}$ pour lesquelles d tourbillons sont présents dans le condensat, puis nous localisons ces tourbillons. Notre méthode est basée sur un développement asymptotique de l'énergie.

Received: 2005-03-02
Published online: 2005-04-15

DOI: 10.1016/j.crma.2005.03.015

Author's affiliations:

Radu Ignat ¹; Vincent Millot ¹

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France

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     title = {Vortices in a 2d rotating {Bose{\textendash}Einstein} condensate},
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     year = {2005},
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     language = {en},
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Radu Ignat; Vincent Millot. Vortices in a 2d rotating Bose–Einstein condensate. Comptes Rendus. Mathématique, Volume 340 (2005) no. 8, pp. 571-576. doi : 10.1016/j.crma.2005.03.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.015/

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