Ginzburg–Landau vortices, Coulomb gases, and Abrikosov lattices

Sylvia Serfaty

doi:10.1016/j.crhy.2014.06.001

Grand Prix Mergier–Bourdeix 2013 de l'Académie des sciences

Ginzburg–Landau vortices, Coulomb gases, and Abrikosov lattices
[Vortex de Ginzburg–Landau, gaz de Coulomb et réseaux d'Abrikosov]

Sylvia Serfaty ^1,²

¹ UPMC (Université Paris-6) & CNRS, UMR 7598 “Laboratoire Jacques-Louis-Lions”, 75005 Paris, France
² Courant Institute, New York University, 251 Mercer st, New York, NY 10012, USA

Comptes Rendus. Physique, Volume 15 (2014) no. 6, pp. 539-546.

Résumé
Abstract

Cet article présente une analyse des vortex dans le modèle de Ginzburg–Landau : les transitions de phase ainsi que les énergies effectives qui gouvernent les structures optimales formées par les vortex, en particulier le réseau d'Abrikosov, sont discutées. Des analogies avec les gaz de Coulomb sont aussi évoquées.

This is a review of a mathematical analysis of vortices in the Ginzburg–Landau model: phase transitions and effective energies that govern optimal patterns formed by the vortices, in particular the Abrikosov lattice, are discussed. Analogies with Coulomb gases are also mentioned.

Publié le : 2014-06-01

DOI : 10.1016/j.crhy.2014.06.001

Keywords: Ginzburg–Landau equations, Superconductivity, Vortices, Abrikosov lattice, Coulomb gas, One-component plasma
Mot clés : Équations de Ginzburg–Landau, Supraconductivité, Vortex, Réseau d'Abrikosov, Gaz de Coulomb, Plasma à un constituant

Affiliations des auteurs :

Sylvia Serfaty ^{1, 2}

¹ UPMC (Université Paris-6) & CNRS, UMR 7598 “Laboratoire Jacques-Louis-Lions”, 75005 Paris, France
² Courant Institute, New York University, 251 Mercer st, New York, NY 10012, USA

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     pages = {539--546},
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Sylvia Serfaty. Ginzburg–Landau vortices, Coulomb gases, and Abrikosov lattices. Comptes Rendus. Physique, Volume 15 (2014) no. 6, pp. 539-546. doi : 10.1016/j.crhy.2014.06.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2014.06.001/

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