Geodesic
Boundary states of the Robin magnetic Laplacian
Documenta mathematica, Tome 29 (2024) no. 5, pp. 1157-1200

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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.
DOI : 10.4171/dm/971
Classification : 81Q10, 35J25, 35P15, 35P20, 35Q40, 35S05
Mots-clés : magnetic Laplacian, Robin boundary condition, spectral analysis, semiclassical analysis 
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     author = {Rayan Fahs and Lo{\"\i}c Le Treust and Nicolas Raymond and San V\~{u} Ngọc},
     title = {Boundary states of the {Robin} magnetic {Laplacian}},
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     pages = {1157--1200},
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Rayan Fahs; Loïc Le Treust; Nicolas Raymond; San Vũ Ngọc. Boundary states of the Robin magnetic Laplacian. Documenta mathematica, Tome 29 (2024) no. 5, pp. 1157-1200. doi: 10.4171/dm/971

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