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H 1 Inhomogeneities and temperature effects in Bose-Einstein condensates

Auteurs : de Bouard, Anne (Auteur de la Conférence)
CIRM (Editeur )

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Bose-Einstein condensate fluctuations stochastic partial differential equation nonlinear Schrödinger equation collapse vortices temperature effects white noise Gibbs measure questions of the audience

Résumé : We will review in this talk some mathematical results concerning stochastic models used by physicist to describe BEC in the presence of fluctuations (that may arise from inhomogeneities in the confinement parameters), or BEC at finite temperature. The results describe the effect of those fluctuations on the structures - e.g. vortices - which are present in the deterministic model, or the convergence to equilibrium in the models at finite temperature. We will also describe the numerical methods which have been developed for those models in the framework of the ANR project Becasim. These are joint works with Reika Fukuizumi, Arnaud Debussche, and Romain Poncet.

Codes MSC :
35Q55 - NLS-like equations (nonlinear Schrödinger)
60H15 - Stochastic partial differential equations
65M06 - Finite difference methods (IVP of PDE)

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 15/07/2016
    Date de captation : 28/06/2016
    Collection : Research talks ; Partial Differential Equations ; Probability and Statistics ; Numerical Analysis and Scientific Computing
    Format : MP4 (.mp4) - HD
    Durée : 00:46:35
    Domaine : PDE ; Probability & Statistics ; Numerical Analysis & Scientific Computing
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-06-28_Bouard.mp4

Informations sur la rencontre

Nom de la rencontre : New challenges in mathematical modelling and numerical simulation of superfluids / Nouveaux défis dans la modélisation mathématique et la simulation numérique de systèmes superfluides
Organisateurs de la rencontre : Danaila, Ionut ; Carles, Rémi ; Weizhu, Bao
Dates : 27/06/16 - 01/07/2016
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1386.html

Citation Data

DOI : 10.24350/CIRM.V.19008603
Cite this video as: de Bouard, Anne (2016). Inhomogeneities and temperature effects in Bose-Einstein condensates. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19008603
URI : http://dx.doi.org/10.24350/CIRM.V.19008603

Voir aussi


  • de Bouard, A., & Fukuizumi, R. (2007). Stochastic fluctuations in the Gross-Pitaevskii equation. Nonlinearity, 20(12), 2823-2844 - http://dx.doi.org/10.1088/0951-7715/20/12/005

  • de Bouard, A., & Fukuizumi, R. (2012). Representation formula for stochastic Schrödinger evolution equations and applications, Nonlinearity, 25(11), 2993-3022 - http://dx.doi.org/10.1088/0951-7715/25/11/2993

  • de Bouard, A., Fukuizumi, R., & Debussche, A. (In preparation). Convergence to equilibrium in BEC -

  • Garnier, J., Abdullaev, F.Kh., & Baizakov, B.B. (2004). Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity. Physical Review A, 69(5), 053607 - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.69.053607

  • Poncet, R., Fukuizumi, R., & de Bouard, A. (2015). Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time. Discrete and Continuous Dynamical Systems. Series B, 20(9), 2793-2817 - http://dx.doi.org/10.3934/dcdsb.2015.20.2793

  • Weiler, C.N., Neely, T.W., Scherer, D.R., Bradley, A.S., Davis, M.J., & Anderson, B.P. (2008). Spontaneous vortices in the fluctuations of Bose-Einstein condensates, Nature, 455, 948-951 - http://dx.doi.org/10.1038/nature07334