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Inhomogeneities and temperature effects in Bose-Einstein condensates
Post-edited
Authors : de Bouard, Anne (Author of the conference)
CIRM (Publisher )
35Q55 - NLS-like equations (nonlinear Schrödinger)
60H15 - Stochastic partial differential equations
65M06 - Finite difference methods (IVP of PDE)
CIRM (Publisher )
Abstract :
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.
MSC Codes : 35Q55 - NLS-like equations (nonlinear Schrödinger)
60H15 - Stochastic partial differential equations
65M06 - Finite difference methods (IVP of PDE)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/07/2016 Conference Date : 28/06/2016 Subseries : Research talks arXiv category : Analysis of PDEs ; Probability Mathematical Area(s) : PDE ; Probability & Statistics ; Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 00:46:35 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-06-28_Bouard.mp4 
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Information on the Event
Event Title : New challenges in mathematical modelling and numerical simulation of superfluids / Nouveaux défis dans la modélisation mathématique et la simulation numérique de systèmes superfluidesEvent Organizers : Danaila, Ionut ; Carles, Rémi ; Weizhu, Bao Dates : 27/06/16 - 01/07/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1386.html
Citation Data
DOI : 10.24350/CIRM.V.19008603Cite 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 |
See Also
- [Multi angle] Polariton graph simulators / Author of the conference Berloff, Natalia.
- [Multi angle] High-order Magnus integrators for non-autonomous linear evolution equations / Author of the conference Thalhammer, Mechthild.
- [Multi angle] Leapfrogging for the axisymmetric Gross-Pitaevskii equation / Author of the conference Smets, Didier.
- [Multi angle] Classical and non-classical flows of superfluids / Author of the conference Barenghi, Carlo.
Bibliography
- 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
