Thin domain limit and counterexamples to strong diamagnetism
Analysis of PDEs
2020-07-24 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We study the magnetic Laplacian and the Ginzburg-Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some non-linear regime, we determine the structure of the order parameter and compute the super-current along the boundary of the sample. Our results are in agreement with what was observed in the Little-Parks experiment, for a thin cylindrical sample.
Keywords
Cite
@article{arxiv.1905.06152,
title = {Thin domain limit and counterexamples to strong diamagnetism},
author = {Bernard Helffer and Ayman Kachmar},
journal= {arXiv preprint arXiv:1905.06152},
year = {2020}
}