Spectral analysis in sheared waveguides | Vidéo | Carmin.tv

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Spectral analysis in sheared waveguides

De Alessandra Verri

Apparaît dans la collection : Spectral Analysis for Quantum Hamiltonians / Analyse Spectrale pour des Hamiltoniens Quantiques

Let $\Omega \subset \mathbb{R}^3$ be a sheared waveguide, i.e., $\Omega$ is built by translating a cross-section (an arbitrary bounded connected open set of $\mathbb{R}^2$ ) in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of $-\Delta_{\Omega}^D$. After that, we state sufficient conditions that give rise to a non-empty discrete spectrum for $-\Delta_{\Omega}^D$. Finally, in case the cross section translates along a broken line in $\mathbb{R}^3$, we prove that the discrete spectrum of $-\Delta_{\Omega}^D$ is finite, furthermore, we show a particular geometry for $\Omega$ which implies that the total multiplicity of the discrete spectrum is equals 1.

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.20127403
Citer cette vidéo Verri, Alessandra (18/01/2024). Spectral analysis in sheared waveguides. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20127403
URL https://dx.doi.org/10.24350/CIRM.V.20127403

Domaine(s)

Théorie spectrale

Bibliographie

SUAREZ BELLO, Diana Carolina et VERRI, Alessandra A. Spectral analysis in broken sheared waveguides. Mathematical Methods in the Applied Sciences. - https://doi.org/10.1002/mma.9914
VERRI, Alessandra A. Spectrum of the Dirichlet Laplacian in sheared waveguides. Zeitschrift für angewandte Mathematik und Physik, 2021, vol. 72, p. 1-12. - http://dx.doi.org/10.1007/s00033-020-01444-z

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