A Model for Vortex Nucleation in the Ginzburg–Landau Equations

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.

Stochastic Quantization of an Abelian Gauge Theory

“…Remark 1.4 With the method developed in this article, it should be straightforward to obtain a local solution theory for such a U(1) theory in two spatial dimensions with "Ginzburg-Landau potentials", that is, with polynomial terms P (|Φ| 2 ) in the Hamiltonian H. These are important models in superconductivity, with the "vortices dynamics" of particular interest; to our best knowledge the stochastic dynamics of vortices have been only defined intuitively so far (see for instance [IS17]).…”