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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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