Γ-stability and vortex motion in type II superconductors

Matthias Kurzke; Daniel Spirn

doi:10.1080/03605302.2010.520182

Γ-stability and vortex motion in type II superconductors

Matthias Kurzke, Daniel Spirn

Mathematics

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4 Scopus citations

Abstract

We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γ-stability result relating the Ginzburg-Landau energy to the renormalized energy.

Original language	English (US)
Pages (from-to)	256-292
Number of pages	37
Journal	Communications in Partial Differential Equations
Volume	36
Issue number	2
DOIs	https://doi.org/10.1080/03605302.2010.520182
State	Published - Feb 2011

Bibliographical note

Funding Information:
The research presented in this article was begun while the authors enjoyed the hospitality of the Hausdorff Research Institute for Mathematics, Bonn. MK was supported by DFG SFB 611. DS was supported by NSF grant DMS-0707714. The authors wish to thank the anonymous referees for numerous suggestions that significantly improved the presentation of the results.

Keywords

Ginzburg-Landau theory
Superconductivity
Vortex dynamics

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AU - Spirn, Daniel

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AB - We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γ-stability result relating the Ginzburg-Landau energy to the renormalized energy.

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Γ-stability and vortex motion in type II superconductors

Abstract

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Keywords

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