English
Inhomogeneities and temperature effects in Bose-Einstein condensates
Post-edited
Auteurs : de Bouard, Anne (Auteur de la Conférence)
CIRM (Editeur )
35Q55 - NLS-like equations (nonlinear Schrödinger)
60H15 - Stochastic partial differential equations
65M06 - Finite difference methods (IVP of PDE)
CIRM (Editeur )
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)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 15/07/2016 Date de captation : 28/06/2016 Sous collection : Research talks arXiv category : Analysis of PDEs ; Probability Domaine : PDE ; Probability & Statistics ; Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 00:46:35 Audience : Researchers Download : https://videos.cirm-math.fr/2016-06-28_Bouard.mp4 
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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 superfluidesOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19008603Citer cette vidéo: 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
- [Multi angle] Polariton graph simulators / Auteur de la Conférence Berloff, Natalia.
- [Multi angle] High-order Magnus integrators for non-autonomous linear evolution equations / Auteur de la Conférence Thalhammer, Mechthild.
- [Multi angle] Leapfrogging for the axisymmetric Gross-Pitaevskii equation / Auteur de la Conférence Smets, Didier.
- [Multi angle] Classical and non-classical flows of superfluids / Auteur de la Conférence Barenghi, Carlo.
Bibliographie
- 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
