Volume 13, Number 1, January-March 2007
|Page(s)||35 - 71|
|Published online||14 February 2007|
Local minimizers with vortex filaments for a Gross-Pitaevsky functional
Math Department, University of Toronto, Toronto, ON M5S 3G3, Canada; email@example.com
Revised: 22 August 2005
This paper gives a rigorous derivation of a functional proposed by Aftalion and Rivière [Phys. Rev. A 64 (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.
Mathematics Subject Classification: 35Q40 / 35B25 / 49Q20
Key words: Gross-Pitaevsky / vortices / Gamma-convergence / Thomas-Fermi limit / rectifiable currents.
© EDP Sciences, SMAI, 2007
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