Boundary states of the Robin magnetic Laplacian

  • Rayan Fahs

    Univ Angers, CNRS, LAREMA, Institut Universitaire de France, SFR MathSTIC, Angers, France
  • Loïc Le Treust

    Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
  • Nicolas Raymond

    Univ Angers, CNRS, LAREMA, Institut Universitaire de France, SFR MathSTIC, Angers, France
  • San Vũ Ngọc

    University of Rennes, CNRS, Rennes, France
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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.

Cite this article

Rayan Fahs, Loïc Le Treust, Nicolas Raymond, San Vũ Ngọc, Boundary states of the Robin magnetic Laplacian. Doc. Math. 29 (2024), no. 5, pp. 1157–1200

DOI 10.4171/DM/971