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

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Boundary states of the magnetic Robin Laplacian

De Nicolas Raymond

Apparaît dans la 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.

Informations sur la vidéo

Date de captation 18/01/2024
Date de publication 01/02/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20127003
Citer cette vidéo 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

Domaine(s)

Bibliographie

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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