Magnetic Vortices, Abrikosov Lattices and Automorphic Functions
Abstract
We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Landau equations. First developed to explain and predict properties of superconductors, these equations form an integral part - Abelean-Higgs component - of the standard model of particle physics and, in general, have a profound influence on physics well beyond their original designation area. %These are a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics. (The latest variant of these equations is the Seiberg - Witten equations.)
Keywords
Cite
@article{arxiv.1308.5440,
title = {Magnetic Vortices, Abrikosov Lattices and Automorphic Functions},
author = {Israel Michael Sigal},
journal= {arXiv preprint arXiv:1308.5440},
year = {2013}
}
Comments
30 pages, 3 figures