On the magnetic laplacian with a piecewise constant magnetic field in ℝ³₊

2022/07/27 by Emanuela L. Giacomelli, Giacomelli, Emanuela L.
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2207.13627

openalex publication_date 2022/07/27 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

We consider the Neumann realization of the magnetic laplacian in ℝ³₊, 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.

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