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arXiv · 2308.16817

Boundary states of the Robin magnetic Laplacian

Rayan Fahs·Loïc Le Treust·Nicolas Raymond·San Vu Ngoc
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Abstract

This article tackles the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semiclassical limit, a uniform description of the spectrum located between the Landau levels is obtained. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal dimensional reduction, our unifying approach allows on the one hand to derive a very precise Weyl law and a proof of quantum magnetic oscillations for excited states, and on the other hand to refine simultaneously old results about the low-lying eigenvalues in the Robin case and recent ones about edge states in the Dirichlet case.

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Rayan Fahs, Loïc Le Treust, Nicolas Raymond, San Vu Ngoc. 2023-08-31. Boundary states of the Robin magnetic Laplacian. https://arxiv.org/abs/2308.16817

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