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On the geometry of Gross-Pitaevski vortex curves for generic data

Authors: José Alberto Montero and Benjamin K. Stephens
Journal: Proc. Amer. Math. Soc. 141 (2013), 3871-3881
MSC (2010): Primary 49K15
Published electronically: July 24, 2013
MathSciNet review: 3091776
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Abstract: We study an energy functional that arises as a $ \Gamma $-limit of the Gross-Pitaevskii (GP) energy. This last functional is often used to model rotating Bose-Einstein condensates, and the functional we study represents the contribution to the GP energy of vortices, or whirlpools, in the condensate. For our energy, we give a rough description of its (local) minimizers using ODE techniques along with an isoperimetric inequality.

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  • 1. Aftalion, A., Vortices in Bose-Einstein Condensates, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, 2006. MR 2228356 (2007g:82078)
  • 2. Brezis, H., Analyse fonctionnelle, deuxième edition, Dunod, 1999.
  • 3. Alama, S., Bronsard, L. and Montero, A., Vortices for a rotating toroidal Bose-Einstein condensate, Arch. Ration. Mech. Anal. 187 (2008), no. 3, 481-522. MR 2372812 (2009d:82015)
  • 4. Federer, H., Geometric measure theory, Springer-Verlag, 1969. MR 0257325 (41:1976)
  • 5. Ignat, R. and Millot, V., Energy expansion and vortex location for a two-dimensional rotating Bose-Einstein condensate, Rev. Math. Phys. 18 (2006), 119-162. MR 2228922 (2007b:58030)
  • 6. Jerrard, R. L., Local minimizers with vortex filaments for a Gross-Pitaevsky functional, ESAIM Control Optim. Calc. Var. 13 (2007), no. 1, 35-71 (electronic). MR 2282101 (2008g:58026)
  • 7. Montero, J. A., Hodge decomposition with degenerate weights and the Gross-Pitaevskii
    J. Funct. Anal. 254 (2008), no. 7, 1926-1973. MR 2397879 (2009h:35028)
  • 8. Pitaevskii, L. and Stringari, S., Bose-Einstein condensation, Oxford University Press, 2003. MR 2012737 (2004i:82038)

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Additional Information

José Alberto Montero
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

Benjamin K. Stephens
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

Received by editor(s): May 3, 2011
Received by editor(s) in revised form: January 16, 2012
Published electronically: July 24, 2013
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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