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Vortex Density Models for Superconductivity and Superfluidity

Author(s): Baldo, S; Jerrard, RL; Orlandi, G; Soner, H Mete

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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. © 2012 Springer-Verlag Berlin Heidelberg.
Publication Date: 1-Jan-2013
Citation: Baldo, S, Jerrard, RL, Orlandi, G, Soner, HM. (2013). Vortex Density Models for Superconductivity and Superfluidity. Communications in Mathematical Physics, 318 (1), 131 - 171. doi:10.1007/s00220-012-1629-2
DOI: doi:10.1007/s00220-012-1629-2
ISSN: 0010-3616
EISSN: 1432-0916
Pages: 131 - 171
Type of Material: Journal Article
Journal/Proceeding Title: Communications in Mathematical Physics
Version: Author's manuscript

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