On the magnetic laplacian with a piecewise constant magnetic field in ${\mathbb{R}}_{+}^3$

Abstract

We consider the Neumann realization of the magnetic laplacian in ${\mathbb{R}}_{+}^3$, in the case in which the magnetic field has a piecewise constant strength and a uniform direction. This operator is expected to be an effective model in studying the threshold to the normal state for a 3D superconductor exposed to a discontinuous magnetic field. We review some recent results above the infimum of the spectrum of the aforementioned operator.

11 pages, contribution to the Proceedings of the Intensive Period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March - May 2022