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Vortices for a Rotating Toroidal Bose–Einstein Condensate

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Abstract

We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid torus of revolution in \({\mathbb{R}}^3\) with starshaped cross-section. We show that for angular speeds ωε = O(|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the torus.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Stan Alama & Lia Bronsard

  2. Department of Mathematics, University of Toronto, Toronto, ON, M5S 3G3, Canada

    J. Alberto Montero

Authors
  1. Stan Alama
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  2. Lia Bronsard
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  3. J. Alberto Montero
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Correspondence to Stan Alama.

Additional information

Communicated by D. Kinderlehrer

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Alama, S., Bronsard, L. & Montero, J.A. Vortices for a Rotating Toroidal Bose–Einstein Condensate. Arch Rational Mech Anal 187, 481–522 (2008). https://doi.org/10.1007/s00205-007-0077-1

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  • DOI: https://doi.org/10.1007/s00205-007-0077-1

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