Local strong magnetic fields and the Little-Parks effect
arXiv:2405.09099
Abstract
Starting from the Ginzburg--Landau model in a planar simply connected domain, with a local compactly supported applied magnetic field, we derive an effective model in the strong field limit, defined on a non-simply connected domain. The effective model features oscillations in the Little-Parks and Aharonov--Bohm spirit. We discuss also a similar question for the lowest eigenvalue of the magnetic Laplacian.
12 pages, to appear in a special issue of "Pure and Applied Functional Analysis"