Published Paper

Inserted: 23 feb 2011
Last Updated: 25 aug 2012

Journal: Archive Rat. Mech. Analysis
Volume: 205
Number: 3
Pages: 699-752
Year: 2012

Abstract:

In this paper we consider the asymptotic behavior of the Ginzburg-Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via $\Gamma$-convergence, a reduced model for the vortex density, and deduce a curvature equation for the vortex lines. In the companion paper 2 we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field $H_{c_1}$, and the critical angular velocity of rotating Bose-Einstein condensates.

Keywords: Ginzburg-Landau, Superconductivity, vortices

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