Properties of a single vortex solution in a rotating Bose Einstein condensate

Amandine Aftalion; Robert L. Jerrard

doi:10.1016/S1631-073X(03)00166-3

Partial Differential Equations

Properties of a single vortex solution in a rotating Bose Einstein condensate
[Propriétés d'une solution à un vortex pour un condensat de Bose Einstein en rotation]

Présenté par : Haı̈m Brezis

Amandine Aftalion ¹ ; Robert L. Jerrard ²

¹ Laboratoire Jacques-Louis Lions, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France
² Department of Mathematics, 100 St George St, University of Toronto, Toronto M5S 3G3, Canada

Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 713-718.

Abstract (VO)
Résumé

In this Note, we study the properties of the line energy for a vortex γ in a Bose Einstein condensate rotating at velocity $Ω$ . The global minimizer is either the vortex free solution or U vortices which exist only for $Ω$ bigger than a critical value. For all values of $Ω$ , we prove the existence of an S type vortex, which is a critical point of the line energy, observed in the experiments. We also prove uniqueness of the minimizer for almost every $Ω$ and a monotonicity property of the curve γ with respect to $Ω$ . The proofs rely on a related isoperimetric problem.

Dans cette Note, nous étudions les propriétés de l'énergie de ligne pour un vortex γ dans un condensat de Bose Einstein en rotation à la vitesse $Ω$ . Nous prouvons que, pour tout $Ω$ , il existe un vortex de type S, qui est un point critique de l'énergie, mais jamais un minimiseur. Le minimiseur global est soit la solution sans vortex soit un vortex en U, qui n'existe que pour $Ω$ plus grand qu'une valeur critique. Nous prouvons également l'unicité des minimiseurs pour presque tout $Ω$ et une propriété de monotonie des courbes γ par rapport à $Ω$ . Les preuves reposent sur un problème de type isopérimétrique.

Reçu le : 2003-03-17
Accepté le : 2003-03-17
Publié le : 2003-04-23

DOI : 10.1016/S1631-073X(03)00166-3

Affiliations des auteurs :

Amandine Aftalion ¹ ; Robert L. Jerrard ²

¹ Laboratoire Jacques-Louis Lions, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France
² Department of Mathematics, 100 St George St, University of Toronto, Toronto M5S 3G3, Canada

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     title = {Properties of a single vortex solution in a rotating {Bose} {Einstein} condensate},
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     doi = {10.1016/S1631-073X(03)00166-3},
     language = {en},
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Amandine Aftalion; Robert L. Jerrard. Properties of a single vortex solution in a rotating Bose Einstein condensate. Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 713-718. doi : 10.1016/S1631-073X(03)00166-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00166-3/

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Cité par 6 documents. Sources : Crossref, zbMATH

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