Geometrical description of vortices in Ginzburg-Landau billiards
arXiv:cond-mat/9907441
Abstract
In these notes we discuss the topological nature of some problems in condensed matter physics. We adopt the language of differential geometry to present this subject and our aim is to develop some intuition towards concepts like curvature, fiber bundles, connexions, characteristic classes and topological invariants. The lectures end with a theoretical analysis of recent experimental results obtained on mesoscopic superconducting films.
36 pages. Lectures delivered at Les Houches, Summer School, Topological aspects of low dimensional systems, July 1998