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.
Vortex density models for Superconductivity and Superfluidity
BALDO, Sisto;ORLANDI, Giandomenico;
2013-01-01
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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