Convergence of Ginzburg-Landau functionals in 3-d superconductivity

TL;DR

This paper analyzes the asymptotic behavior of the 3D Ginzburg-Landau model for superconductivity, deriving a reduced vortex density model and a curvature equation for vortex lines using Gamma-convergence.

Contribution

It provides a rigorous derivation of a reduced vortex density model and a curvature equation for vortex lines in 3D superconductivity via Gamma-convergence.

Findings

Derived a reduced model for vortex density

Established a curvature equation for vortex lines

Analyzed energy regimes in 3D 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 {\Gamma}-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.