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Vortex Density Models for Superconductivity and Superfluidity

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Abstract

We study some functionals that describe the density of vortex lines in superconductors subject to an applied magnetic field, and in Bose-Einstein condensates subject to rotational forcing, in quite general domains in 3 dimensions. These functionals are derived from more basic models via Gamma-convergence, here and in the companion paper (Baldo et al. in Arch Rat Mech Anal 205(3):699–752, 2012). In our main results, we use these functionals to obtain leading order descriptions of the first critical applied magnetic field (for superconductors) and forcing (for Bose-Einstein), above which ground states exhibit nontrivial vorticity, as well as a characterization of the vortex density in terms of a non local vector-valued generalization of the classical obstacle problem.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    S. Baldo & G. Orlandi

  2. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

    R. L. Jerrard

  3. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    H. M. Soner

Authors
  1. S. Baldo
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  2. R. L. Jerrard
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  3. G. Orlandi
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  4. H. M. Soner
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Correspondence to R. L. Jerrard.

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Communicated by I. M. Sigal

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Baldo, S., Jerrard, R.L., Orlandi, G. et al. Vortex Density Models for Superconductivity and Superfluidity. Commun. Math. Phys. 318, 131–171 (2013). https://doi.org/10.1007/s00220-012-1629-2

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  • DOI: https://doi.org/10.1007/s00220-012-1629-2

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