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Boundary states of the magnetic Robin Laplacian

By Nicolas Raymond

Appears in collection : Spectral Analysis for Quantum Hamiltonians / Analyse Spectrale pour des Hamiltoniens Quantiques

In this (hopefully) blackboard talk, we will discuss 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, I will explain how to get a uniform description of the spectrum located between the Landau levels. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal dimensional reduction, I will explain how to derive a very precise Weyl law and a proof of quantum magnetic oscillations for excited states, and also how to refine simultaneously old results about the low-lying eigenvalues in the Robin case and recent ones about edge states in the Dirichlet case. Joint work with R. Fahs, L. Le Treust and S. Vu Ngoc.

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Citation data

  • DOI 10.24350/CIRM.V.20127003
  • Cite this video Raymond, Nicolas (18/01/2024). Boundary states of the magnetic Robin Laplacian. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20127003
  • URL https://dx.doi.org/10.24350/CIRM.V.20127003


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