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

2023/06/30 by Alfa, Khaled Abou, Aafarani, Maha, Hérau, Frédéric +1
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2306.17446

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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