Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field

2022/03/11 by Hérau, Frédéric, Raymond, Nicolas
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2203.06048

Abstract

This article deals with the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and in the semiclassical limit, we establish a four-term asymptotic expansion of the low-lying eigenvalues, involving a geometric quantity along the apparent contour of the domain in the direction of the field. In particular, we prove that they are simple.

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