A Model for Vortex Nucleation in the Ginzburg–Landau Equations

Gautam Iyer; Daniel Spirn

doi:10.1007/s00332-017-9391-4

A Model for Vortex Nucleation in the Ginzburg–Landau Equations

Gautam Iyer, Daniel Spirn

Mathematics

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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.

Original language	English (US)
Pages (from-to)	1933-1956
Number of pages	24
Journal	Journal of Nonlinear Science
Volume	27
Issue number	6
DOIs	https://doi.org/10.1007/s00332-017-9391-4
State	Published - 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).

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

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Primary 35Q56
Secondary 60H30

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A Model for Vortex Nucleation in the Ginzburg–Landau Equations

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