Counting eigenvalues below the lowest Landau level

2024/06/10 by Fournais, Soeren, Kachmar, Ayman · 1 citation
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2406.06411

Abstract

For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component and a Dirichlet condition on the other, one gets fewer such eigenvalues than when imposing Neumann boundary conditions on the two components. We quantify this observation for two models: the strip and the annulus. In both models one can separate variables and deal with a family of fiber operators, thereby reducing the problem to counting band functions, the eigenvalues of the fiber operators.

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• Low-lying eigenvalues in the semiclassical limit of a Schrödinger operator with an inverse square potential, and non-asymptotic a-zeros of Kummer functions

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