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

Frédéric Hérau; Nicolas Raymond

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arXiv · 2203.06048

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

Frédéric Hérau·Nicolas Raymond

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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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BibTeX RIS

Frédéric Hérau, Nicolas Raymond. 2022-03-11. Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field. https://arxiv.org/abs/2203.06048

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