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Semiclassical behaviour of quantum eigenstates - lecture 1

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Auteurs : Rivière, Gabriel (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : Given a quantum Hamiltonian, I will explain how the dynamical properties of the underlying classical Hamiltonian affect the behaviour of quantum eigenstates in the semiclassical limit. I will mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. I will introduce tools from microlocal analysis and show how to use them in order to illustrate the classical-quantum correspondance and to compare properties of completely integrable and chaotic systems.

Codes MSC :
35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37N20 - Dynamical systems in other branches of physics
58J50 - Spectral problems; spectral geometry; scattering theory
81Q50 - Quantum chaos [See also 37Dxx]
58J51 - Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 24/05/2019
    Date de captation : 22/04/2019
    Sous collection : Research School
    arXiv category : Dynamical Systems ; Mathematical Physics
    Domaine : Mathematical Physics ; Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Durée : 01:32:23
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-04-22_Riviere_Part1.mp4

Informations sur la Rencontre

Nom de la rencontre : Du quantique au classique / From Quantum to Classical
Organisateurs de la rencontre : Nonnenmacher, Stéphane ; Sabin, Julien
Dates : 22/04/2019 - 26/04/2019
Année de la rencontre : 2019
URL Congrès : https://conferences.cirm-math.fr/1982.html

Données de citation

DOI : 10.24350/CIRM.V.19527603
Citer cette vidéo: Rivière, Gabriel (2019). Semiclassical behaviour of quantum eigenstates - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19527603
URI : http://dx.doi.org/10.24350/CIRM.V.19527603

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