Convergence of Ginzburg-Landau functionals in 3-d superconductivity

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 Γ-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.

45 pages

References in corpus (1)

• Vortex density models for superconductivity and superfluidity

Cited by in corpus (6)

• Ginzburg-Landau vortices, Coulomb Gases, and Renormalized Energies
• Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
• Vortex density models for superconductivity and superfluidity
• Concentration Behavior and Lattice Structure of Surface Superconductivity
• 3D vortex approximation construction and $\epsilon$-level estimates for the Ginzburg-Landau functional
• On the first critical field in the 3D Ginzburg-Landau model of superconductivity