Boundary states of the magnetic Robin Laplacian | Vidéo | Carmin.tv

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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.

Information about the video

Date of recording 18/01/2024
Date of publication 01/02/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

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

Domain(s)

Bibliography

FAHS, Rayan, TREUST, Loïc Le, RAYMOND, Nicolas, et al. Boundary states of the Robin magnetic Laplacian. arXiv preprint arXiv:2308.16817, 2023. - https://doi.org/10.48550/arXiv.2308.16817

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