Vortices in the Ginzburg-Landau model of superconductivity

Sylvia Serfaty

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We review some mathematical results on the Ginzburg-Landau model with and without magnetic field. The Ginzburg-Landau energy is the standard model for superconductivity, able to predict the existence of vortices (which are quantized, topological defects) in certain regimes of the applied magnetic field. We focus particularly on deriving limiting (or reduced) energies for the Ginzburg-Landau energy functional, depending on the various parameter regimes, in the spirit of Γ-convergence. These passages to the limit allow to perform a sort of dimension-reduction and to deduce a rather complete characterization of the behavior of vortices for energy-minimizers, in agreement with the physics results. We also describe the behavior of energy critical points, the stability of the solutions, the motion of vortices for solutions of the gradient-flow of the Ginzburg-Landau energy, and show how they are also governed by those of the limiting energies.

Original languageEnglish (US)
Title of host publicationInternational Congress of Mathematicians, ICM 2006
Pages267-290
Number of pages24
Volume3
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

Fingerprint

Ginzburg-Landau Model
Superconductivity
Vortex
Ginzburg-Landau
Energy
Limiting
Magnetic Field
Topological Defects
Gradient Flow
Dimension Reduction
Energy Functional
Minimizer
Sort
Standard Model
Deduce
Critical point
Physics
Predict
Motion

Keywords

  • Γ-convergence
  • Ginzburg-Landau equations
  • Superconductivity
  • Variational methods
  • Vortices

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Serfaty, S. (2006). Vortices in the Ginzburg-Landau model of superconductivity. In International Congress of Mathematicians, ICM 2006 (Vol. 3, pp. 267-290)

Vortices in the Ginzburg-Landau model of superconductivity. / Serfaty, Sylvia.

International Congress of Mathematicians, ICM 2006. Vol. 3 2006. p. 267-290.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Serfaty, S 2006, Vortices in the Ginzburg-Landau model of superconductivity. in International Congress of Mathematicians, ICM 2006. vol. 3, pp. 267-290, 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain, 8/22/06.
Serfaty S. Vortices in the Ginzburg-Landau model of superconductivity. In International Congress of Mathematicians, ICM 2006. Vol. 3. 2006. p. 267-290
Serfaty, Sylvia. / Vortices in the Ginzburg-Landau model of superconductivity. International Congress of Mathematicians, ICM 2006. Vol. 3 2006. pp. 267-290
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