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H 1 Estimates on the molecular dynamics for the predissociation process

Auteurs : Martinez, André (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We study the survival probability associated with a semiclassical matrix Schrödinger operator that models the predissociation of a general molecule in the Born-Oppenheimer approximation. We show that it is given by its usual time-dependent exponential contribution, up to a reminder term that is small in the semiclassical parameter and for which we find the main contribution. The result applies in any dimension, and in presence of a number of resonances that may tend to infinity as the semiclassical parameter tends to 0.
    This is a joint work with Ph. Briet.

    Codes MSC :
    35J10 - Schrödinger operator
    35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
    47A75 - Eigenvalue problems (linear operators)
    81Q15 - Perturbation theories for operators and differential equations
    35B34 - Resonances in solutions of PDE

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 21/01/16
      Date de captation : 18/12/15
      Collection : Research talks ; Exposés de recherche ; Partial Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 00:48:53
      Domaine : PDE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-12-18_Martinez.mp4

    Informations sur la rencontre

    Nom de la rencontre : Semiclassical analysis and non-self-adjoint operators / Analyse semi-classique et opérateurs non-autoadjoints
    Organisateurs de la rencontre : Fujiie, Setsuro ; Hérau, Frédéric ; Nicoleau, François ; Ramond, Thierry ; Viola, Joe ; Vu Ngoc, San
    Dates : 14/12/15 - 18/12/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1230.html

    Citation Data

    DOI : 10.24350/CIRM.V.18911303
    Cite this video as: Martinez, André (2015). Estimates on the molecular dynamics for the predissociation process. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18911303
    URI : http://dx.doi.org/10.24350/CIRM.V.18911303


    Bibliographie

    1. Briet, P., & Martinez, A. (2015). Estimates on the molecular dynamics for the predissociation process. - http://arxiv.org/abs/1503.05507

    2. Cattaneo, L., Graf, G. M., & Hunziker, W. (2006). A general resonance theory based on Mourre's inequality. Annales Henri Poincaré, 7(1), 583-601 - http://dx.doi.org/10.1007/s00023-005-0261-5

    3. Costin, O., & Soffer, A. (2001). Resonance theory for Shrodinger operators. Communications in Mathematical Physics, 224(1), 133-152 - http://dx.doi.org/10.1007/s002200100558

    4. Herbst, I. (1980). Exponential decay in the Stark effect. Communications in Mathematical Physics, 75(3), 197-205 - http://dx.doi.org/10.1007/bf01212708

    5. Hunziker, W. (1990). Resonances, metastable states and exponential decay laws in perturbation theory. Communications in Mathematical Physics, 132(1), 177-182 - http://dx.doi.org/10.1007/bf02278006

    6. Jensen, A., & Nenciu, G. (2006). The Fermi golden rule and its form at thresholds in odd dimensions. Communications in Mathematical Physics, 261, 693-727 - http://dx.doi.org/10.1007/s00220-005-1428-0

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