A Model for Vortex Nucleation in the Ginzburg–Landau Equations

Gautam Iyer, Daniel Spirn

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1933-1956
Number of pages24
JournalJournal of Nonlinear Science
Issue number6
StatePublished - Dec 1 2017

Bibliographical note

Funding 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

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