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.
Original language | English (US) |
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Pages (from-to) | 131-171 |
Number of pages | 41 |
Journal | Communications In Mathematical Physics |
Volume | 318 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2013 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics