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Local minimizers with vortex filaments for aGross-Pitaevsky functional

Published online by Cambridge University Press:  14 February 2007

Robert L. Jerrard
Robert L. Jerrard*
Affiliation:
Math Department, University of Toronto, Toronto, ON M5S 3G3, Canada; rjerrard@math.toronto.edu
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Abstract

This paper gives a rigorous derivation of a functional proposed by Aftalion and Rivière [Phys. Rev. A64 (2001) 043611] to characterize the energy of vortex filaments in a rotationally forced Bose-Einstein condensate. This functional is derived as a Γ-limit of scaled versions of the Gross-Pitaevsky functional for the wave function of such a condensate. In most situations, the vortex filament energy functional is either unbounded below or has only trivial minimizers, but we establish the existence of large numbers of nontrivial local minimizers and we prove that, given any such local minimizer, the Gross-Pitaevsky functional has a local minimizer that is nearby (in a suitable sense) whenever a scaling parameter is sufficiently small.

Keywords

Gross-PitaevskyvorticesGamma-convergenceThomas-Fermi limitrectifiable currents.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 35 - 71
Copyright
© EDP Sciences, SMAI, 2007

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References

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