Article Dans Une Revue Documenta Mathematica Année : 2024

Boundary states of the Robin magnetic Laplacian

Résumé

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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Dates et versions

hal-04192966 , version 1 (31-08-2023)

Identifiants

Citer

Rayan Fahs, Loïc Le Treust, Nicolas Raymond, San Vũ Ngọc. Boundary states of the Robin magnetic Laplacian. Documenta Mathematica, 2024, 29 (5), pp.1157-1200. ⟨10.4171/DM/971⟩. ⟨hal-04192966⟩
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