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
[Tourbillons dans un condensat de Bose–Einstein 2d en rotation]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2005-03-02
Publié le : 2005-04-15

DOI : 10.1016/j.crma.2005.03.015

Affiliations des auteurs :

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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     author = {Radu Ignat and Vincent Millot},
     title = {Vortices in a 2d rotating {Bose{\textendash}Einstein} condensate},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {571--576},
     publisher = {Elsevier},
     volume = {340},
     number = {8},
     year = {2005},
     doi = {10.1016/j.crma.2005.03.015},
     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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