Vortices in the Ginzburg-Landau model of superconductivity

Prof. Sylvia Serfaty (Paris 6 / Courant Institute, New York)

March 06, 2014, 14:15 - 16:00
March 07, 2014, 10:15 - 12:00
March 10, 2014, 14:15 - 16:00
March 11, 2014, 10:15 - 12:00
March 17, 2014, 14:15 - 16:00
March 18, 2014, 10:15 - 12:00

All lectures take place at HG G 19.1

This is the continuation of Prof. Serfaty's Nachdiplom lecture of Spring 2013, but the course is structured so that it is not necessary to have attended the lecture in order to follow the minicourse.

Abstract

In the Ginzburg-Landau model of superconductivity, quantized vortices appear when the parameter corresponding to the intensity of the applied magnetic field is large enough. These vortices repel each other and tend to organize themselves in perfect triangular lattices, called „Abrikosov lattices“. This minicourse is aimed at describing some recent results towards justifying the Abrikosov lattices in minimizers of the two-dimensional model. It will start with some heuristics on the onset of these vortices, continue with the main mathematical tools that can be used to understand it rigorously, then derive the leading order „mean field model“ which describes the average density of vortices, and finish with a description of results on the microscopic behavior of the vortices and the lattice problem. Comparisons will be drawn with Coulomb gases.
This is based on joint works with Etienne Sandier.