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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.

Original languageEnglish
JournalAnnales Henri Poincare
Pages (from-to)2021-2068
Number of pages48
Publication statusPublished - 1 Jul 2018

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