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Post-edited Spectral theory and semi-classical analysis for the complex Schrödinger operator

Auteurs : Helffer, Bernard (Auteur de la Conférence)
CIRM (Editeur )

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complex Schrödinger operator nuclear magnetic resonance complex Airy operator semi-group of operators pseudo-spectrum Schatten class completness of eigenfunction Bloch-Torrey operator / semi-classical analysis quasi-modes questions of the audience

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

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 15/06/17
    Date de captation : 07/06/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:42:04
    Domaine : PDE ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-06-07_Helffer.mp4

Informations sur la rencontre

Nom du congrès : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
Organisteurs Congrès : Krejcirik, David ; Siegl, Petr
Dates : 05/06/17 - 09/06/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1596.html

Citation Data

DOI : 10.24350/CIRM.V.19180803
Cite this video as: 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

Voir aussi


  1. Almog, Y., Grebenkov, D., & Helffer, B. (2017). On a Schrödinger operator with a purely imaginary potential in the semiclassical limit. <arXiv:1703.07733> - https://arxiv.org/abs/1703.07733