Discrete spectrum of the magnetic Laplacian on perturbed half-planes

2022/08/29 by Bonnaillie-Noël, Virginie, Fournais, Søren, Kachmar, Ayman +1
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2208.13646

Abstract

The existence of bound states for the magnetic Laplacian in unbounded domains can be quite challenging in the case of a homogeneous magnetic field. We provide an affirmative answer for almost flat corners and slightly curved half-planes when the total curvature of the boundary is positive.

Related

• Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers
• Edge States for the magnetic Laplacian in domains with smooth boundary
• Geometric bounds for the magnetic Neumann eigenvalues in the plane
• The magnetic Laplacian on the Disc for strong magnetic fields
• Inequalities for the lowest magnetic Neumann eigenvalue