English

Magnetic Vortices, Abrikosov Lattices and Automorphic Functions

Mathematical Physics 2013-08-27 v1 math.MP Pattern Formation and Solitons Quantum Physics

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