# Institut for Matematik

## Eigenstates of the Neumann Magnetic Laplacian with Vanishing Magnetic Field

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• Jean Philippe Miqueu

This paper is devoted to the spectral analysis of the magnetic Laplacian with semiclassical parameter h> 0 , defined on a bounded and regular domain Ω of R2 with Neumann magnetic boundary condition, in the case when the magnetic field vanishes along a smooth curve intersecting ∂Ω. We investigate the behavior of the eigenvalues and the associated eigenfunctions when the semiclassical parameter h tends to 0. We provide a one term asymptotic of the first eigenvalue as well as a full asymptotic expansion of the bottom of the spectrum as h→ 0.

Originalsprog Engelsk Annales Henri Poincare 19 7 2021-2068 48 1424-0637 https://doi.org/10.1007/s00023-018-0681-7 Udgivet - 1 jul. 2018

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ID: 143691018