Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text

Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0

Comptes Rendus Mathématique
Volume 336, n° 9
pages 713-718 (mai 2003)
Doi : 10.1016/S1631-073X(03)00166-3
Received : 17 Mars 2003 ;  accepted : 17 Mars 2003
Properties of a single vortex solution in a rotating Bose Einstein condensate

Amandine  Aftalion a ,  Robert L.  Jerrard b
aLaboratoire Jacques-Louis Lions, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France 
bDepartment of Mathematics, 100 St George St, University of Toronto, Toronto M5S 3G3, Canada 


In this Note, we study the properties of the line energy for a vortex   in a Bose Einstein condensate rotating at velocity  . The global minimizer is either the vortex free solution or   vortices which exist only for   bigger than a critical value. For all values of  , we prove the existence of an   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   and a monotonicity property of the curve   with respect to  . The proofs rely on a related isoperimetric problem. To cite this article: A. Aftalion, R.L. Jerrard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).


Dans cette Note, nous étudions les propriétés de l'énergie de ligne pour un vortex   dans un condensat de Bose Einstein en rotation à la vitesse  . Nous prouvons que, pour tout  , il existe un vortex de type  , 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  , qui n'existe que pour   plus grand qu'une valeur critique. Nous prouvons également l'unicité des minimiseurs pour presque tout   et une propriété de monotonie des courbes   par rapport à  . Les preuves reposent sur un problème de type isopérimétrique. Pour citer cet article : A. Aftalion, R.L. Jerrard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

© 2003  Académie des sciences@@#104156@@

EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Article Outline
You can move this window by clicking on the headline