Polya's conjecture in the presence of a constant magnetic field

2007/10/04 by Rupert L. Frank, Michael Loss, Frank, Rupert L. +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0710.1078

openalex publication_date 2007/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Polya's conjecture is not true in the presence of a magnetic field.

Cited by

• 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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