English
Spectral theory and semi-classical analysis for the complex Schrödinger operator
Post-edited
Auteurs : Helffer, Bernard (Auteur de la conférence)
CIRM (Editeur )
35J10 - Schrödinger operator
35P10 - Completeness of eigenfunctions, eigenfunction expansions for PD operators
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
47A10 - Spectrum and resolvent of linear operators
82D55 - Superconductors
81Q12 - Non-selfadjoint operator theory in quantum theory
CIRM (Editeur )
Résumé :
We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.
Codes MSC : 35J10 - Schrödinger operator
35P10 - Completeness of eigenfunctions, eigenfunction expansions for PD operators
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
47A10 - Spectrum and resolvent of linear operators
82D55 - Superconductors
81Q12 - Non-selfadjoint operator theory in quantum theory
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 15/06/17 Date de Captation : 07/06/17 Sous Collection : Research talks Catégorie arXiv : Spectral Theory ; Mathematical Physics Domaine(s) : EDP ; Physique Mathématique Format : MP4 (.mp4) - HD Durée : 00:42:04 Audience : Chercheurs Download : https://videos.cirm-math.fr/2017-06-07_Helffer.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjointsOrganisateurs de la Rencontre : Krejcirik, David ; Siegl, Petr Dates : 05/06/17 - 09/06/17 Année de la rencontre : 2017 URL de la Rencontre : http://conferences.cirm-math.fr/1596.html
Données de citation
DOI : 10.24350/CIRM.V.19180803Citer cette vidéo: Helffer, Bernard (2017). Spectral theory and semi-classical analysis for the complex Schrödinger operator. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19180803 URI : http://dx.doi.org/10.24350/CIRM.V.19180803 |
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Bibliographie
- Almog, Y., Grebenkov, D., & Helffer, B. (2017). On a Schrödinger operator with a purely imaginary potential in the semiclassical limit.
