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Ginzburg-Landau vortices: the static model. (English) Zbl 1027.35131
Séminaire Bourbaki. Volume 1999/2000. Exposés 865-879. Paris: Société Mathématique de France, Astérisque 276, 73-103, Exp. No. 868 (2002).
This paper studies some mathematical questions about superconductivity starting from the Ginzburg-Landau model. The author considers only the two-dimensional case which is the minimal dimension to observe vortices. The aim is to understand the fundamental states of the functional \(J\) (energy functional for a superconductor). More precisely the objective is to identify the zero set of a solution minimizing \(J\). A part of this work is devoted to the study of the Ginzburg-Landau free energy without interaction with the external field. Answers to the conjectures of Jaffe and Taubes in the London limit are given. The third part is devoted to the study of the functional \(G\) satisfying the gauge invariance. The vorticity becomes a variable of the system.
For the entire collection see [Zbl 0981.00011].

MSC:
35Q56 Ginzburg-Landau equations
49R50 Variational methods for eigenvalues of operators (MSC2000)
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
82D55 Statistical mechanical studies of superconductors
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