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H 1 Combined mean-field and semiclassical limits large fermionic system

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    Résumé : In this talk I will present the approach that using time evolution of Husimi measure of the N particle wave function to get the convergence of Schrödinger to Vlasov equation in the mean field and semiclassical regime. By a reformulation of the many particle Schrödinger equation, one can get a Vlasov ‘like’ kinetic equation for Husimi measure. Then the convergence will be obtained by doing appropriate error estimates in comparing these two dynamics. In this first stage result, the estimates have been obtained for regular solutions. This is a joint work with Jinyeop Lee and Matthew Liew.

    Keywords : Schrödinger equation; Vlasov equation; Husimi measure; convergence

    Codes MSC :
    81Q05 - Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
    81V25 - Other elementary particle theory
    35Q83 - Vlasov-like equations

    Ressources complémentaires :

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 26/11/2019
      Date de captation : 24/10/2019
      Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 00:48:18
      Domaine : Analysis and its Applications ; PDE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-10-24_Li Chen.mp4

    Informations sur la rencontre

    Nom de la rencontre : The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters / Analyse des systèmes complexes: grands systèmes coulombiens et systèmes apparentés
    Dates : 21/10/2019 - 25/10/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2066.html

    Citation Data

    DOI : 10.24350/CIRM.V.19571503
    Cite this video as: (2019). Combined mean-field and semiclassical limits large fermionic system. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19571503
    URI : http://dx.doi.org/10.24350/CIRM.V.19571503

    Voir aussi


    1. CHEN, Li, LEE, Jinyeop, et LIEW, Matthew. Combined mean-field and semiclassical limits of large fermionic systems. arXiv preprint arXiv:1910.09892, 2019. - https://arxiv.org/abs/1910.09892