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Inhomogeneities and temperature effects in Bose-Einstein condensates

De Anne de Bouard

Apparaît également dans la collection : New challenges in mathematical modelling and numerical simulation of superfluids / Nouveaux défis dans la modélisation mathématique et la simulation numérique de systèmes superfluides

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.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.19008603
  • Citer cette vidéo de Bouard, Anne (28/06/2016). Inhomogeneities and temperature effects in Bose-Einstein condensates. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19008603
  • URL https://dx.doi.org/10.24350/CIRM.V.19008603

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

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