On the variations of the vortex number in a periodic Ginzburg-Landau model (Q2795523)

This paper deals with the study of the variations of the number of vortices contained in the minimizer of a two-dimensional Ginzburg-Landau functional describing a Type-II superconductor in the London limit, with periodic conditions on the boundary of the sample. Under the hypothesis that the sample is rectangular with height small enough the author establishes that the number of vortices contained in the minimizer of the periodic Ginzburg-Landau functional jumps by unit step as the applied magnetic field increases. Next, this problem is converted into the study of the associated renormalized energy. The final part of this paper includes a discussion of the corresponding one-dimensional model.