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.
Bibliographical noteFunding Information:
This material is based upon work partially supported by the National Science Foundation (through Grants DMS-1252912 to GI, and DMS-0955687, DMS-1516565 to DS), the Simons Foundation (through Grant #393685 to GI), the Center for Nonlinear Analysis (through Grant NSF OISE-0967140), and the Institute for Mathematics and Applications (IMA).
- Primary 35Q56
- Secondary 60H30