m
• E

F Nous contacter

0

Multi angle

H 1 Localization of eigenfunctions via an effective potential

Auteurs : Jerison, David (Auteur de la Conférence)
CIRM (Editeur )

Résumé : We discuss joint work with Doug Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator $L = divA\nabla + V$ on a Lipschitz domain $\Omega$ and, more generally, on manifolds with and without boundary. The eigenfunctions of $L$ are often localized, as a result of disorder of the potential $V$, the matrix of coefficients $A$, irregularities of the boundary, or all of the above. In earlier work, Filoche and Mayboroda introduced the function $u$ solving $Lu = 1$, and showed numerically that it strongly reflects this localization. In this talk, we deepen the connection between the eigenfunctions and this landscape function $u$ by proving that its reciprocal $1/u$ acts as an effective potential. The effective potential governs the exponential decay of the eigenfunctions of the system and delivers information on the distribution of eigenvalues near the bottom of the spectrum.

Codes MSC :
35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
47A75 - Eigenvalue problems (linear operators)
81Q10 - Selfadjoint operator theory in quantum theory, including spectral analysis
81Vxx - Applications of quantum theory to specific physical systems

 Informations sur la Vidéo Langue : Anglais Date de publication : 06/10/2017 Date de captation : 05/10/2017 Collection : Research talks ; Partial Differential Equations ; Mathematical Physics Format : MP4 Durée : 00:55:29 Domaine : Mathematical Physics ; PDE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2017-10-05_Jerison.mp4 Informations sur la rencontre Nom de la rencontre : Harmonic analysis and geometric measure theory / Analyse harmonique et théorie géométrique de la mesureOrganisateurs de la rencontre : Bernicot, Frédéric ; Durand-Cartagena, Estibalitz ; Lemenant, Antoine ; Pajot, Hervé ; Rigot, SéverineDates : 02/10/2017 - 06/10/2017 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1685.htmlCitation Data DOI : 10.24350/CIRM.V.19226303 Cite this video as: Jerison, David (2017). Localization of eigenfunctions via an effective potential. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19226303 URI : http://dx.doi.org/10.24350/CIRM.V.19226303

### Voir aussi

Bibliographie

1. Arnold, D.N., David, G., Jerison, D., Mayboroda, S., & Filoche, M. (2016). Effective confining potential of quantum states in disordered media. - https://arxiv.org/abs/1505.02684

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z