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Combined mean-field and semiclassical limits large fermionic system
Multi angle
Authors : Chen, Li (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2066/Slides/LiChen.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : Keywords : Schrödinger equation; Vlasov equation; Husimi measure; convergence
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2066/Slides/LiChen.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 26/11/2019 Conference Date : 24/10/2019 Subseries : Research talks arXiv category : Mathematical Physics Mathematical Area(s) : Analysis and its Applications ; PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:48:18 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-24_Li Chen.mp4 
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Information on the Event
Event Title : The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters / Analyse des systèmes complexes: grands systèmes coulombiens et systèmes apparentésEvent Organizers : Barbaroux, Jean-Marie ; Panati, Annalisa ; Siedentop, Heinz Dates : 21/10/2019 - 25/10/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2066.html
Citation Data
DOI : 10.24350/CIRM.V.19571503Cite this video as: Chen, Li (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 |
See Also
- [Multi angle] Microscopic description of Coulomb gases / Author of the conference Serfaty, Sylvia.
- [Multi angle] From the many-body quantum dynamics to the Vlasov equation / Author of the conference Saffirio, Chiara.
- [Multi angle] A critical Poincaré-Sobolev inequality / Author of the conference van den Bosch, Hanne.
- [Post-edited] The local density approximation in density functional theory / Author of the conference Seiringer, Robert.
Bibliography
- 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
