English
Estimates on the molecular dynamics for the predissociation process
Multi angle
Auteurs : Martinez, André (Auteur de la conférence)
CIRM (Editeur )
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
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 : This is a joint work with Ph. Briet.
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 21/01/16 Date de Captation : 18/12/15 Sous Collection : Research talks Catégorie arXiv : Spectral Theory ; Mathematical Physics Domaine(s) : EDP ; Physique Mathématique Format : MP4 (.mp4) - HD Durée : 00:48:53 Audience : Chercheurs Download : https://videos.cirm-math.fr/2015-12-18_Martinez.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Semiclassical analysis and non-self-adjoint operators / Analyse semi-classique et opérateurs non-autoadjointsOrganisateurs 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 de la Rencontre : http://conferences.cirm-math.fr/1230.html
Données de citation
DOI : 10.24350/CIRM.V.18911303Citer cette vidéo: 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
- Briet, P., & Martinez, A. (2015). Estimates on the molecular dynamics for the predissociation process.
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- 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
- Herbst, I. (1980). Exponential decay in the Stark effect. Communications in Mathematical Physics, 75(3), 197-205 - http://dx.doi.org/10.1007/bf01212708
- 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
- 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
