Inserted: 3 jan 2012
Last Updated: 18 mar 2013
Journal: Comm. Math. Physics
Links: link at Springer url
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 4. In our main results, we use these functionals to obtain descriptions of the 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.
Keywords: Gamma-convergence, Superconductivity, vortices, Bose-Einstein condensation