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arXiv · 2306.17446

Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions

Khaled Abou Alfa·Maha Aafarani·Frédéric Hérau·Nicolas Raymond
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Abstract

This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the eigenfunctions near the boundary), we establish a semiclassical expansion of the lowest eigenvalues. In particular, we prove that the eigenvalues become simple in the semiclassical limit.

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Khaled Abou Alfa, Maha Aafarani, Frédéric Hérau, Nicolas Raymond. 2023-06-30. Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions. https://arxiv.org/abs/2306.17446

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