A model for vortex nucleation in the Ginzburg-Landau equations

TL;DR

This paper develops a heuristic model for vortex nucleation in the Ginzburg-Landau equations, analyzing boundary vortex dynamics, dipole interactions, and the effects of perturbations on vortex formation.

Contribution

It introduces a new heuristic equation for vortex dynamics near boundaries and dipoles, and studies vortex nucleation under small random perturbations.

Findings

Derived a heuristic vortex dynamics equation near boundaries.

Analyzed vortex nucleation under stochastic perturbations.

Provided insights into the transition between local and global energy minimizers.

Abstract

This paper studies questions related to the dynamic transition between local and global minimizers in the Ginzburg-Landau theory of superconductivity. We derive a heuristic equation governing the dynamics of vortices that are close to the boundary, and of dipoles with small inter vortex separation. We consider a small random perturbation of this equation, and study the asymptotic regime under which vortices nucleate.