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The quantum Vlasov equation
Multi angle
Authors : Mauser, Norbert (Author of the conference)
CIRM (Publisher )
35J10 - Schrödinger operator
35Q40 - PDEs in connection with quantum mechanics
81Q20 - Semi-classical techniques in quantum theory, including WKB and Maslov methods
81S30 - Phase space methods including Wigner distributions, etc.
CIRM (Publisher )
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Abstract :
We present the Quantum Vlasov or Wigner equation as a "phase space" presentation of quantum mechanics that is close to the classical Vlasov equation, but where the "distribution function" $w(x,v,t)$ will in general have also negative values.
We discuss the relation to the classical Vlasov equation in the semi-classical asymptotics of small Planck's constant, for the linear case [2] and for the nonlinear case where we couple the quantum Vlasov equation to the Poisson equation [4, 3, 5] and [1].
Recently, in some sort of "inverse semiclassical limit" the numerical concept of solving Schrödinger-Poisson as an approximation of Vlasov-Poisson attracted attention in cosmology, which opens a link to the "smoothed Schrödinger/Wigner numerics" of Athanassoulis et al. (e.g. [6]).
MSC Codes : We discuss the relation to the classical Vlasov equation in the semi-classical asymptotics of small Planck's constant, for the linear case [2] and for the nonlinear case where we couple the quantum Vlasov equation to the Poisson equation [4, 3, 5] and [1].
Recently, in some sort of "inverse semiclassical limit" the numerical concept of solving Schrödinger-Poisson as an approximation of Vlasov-Poisson attracted attention in cosmology, which opens a link to the "smoothed Schrödinger/Wigner numerics" of Athanassoulis et al. (e.g. [6]).
35J10 - Schrödinger operator
35Q40 - PDEs in connection with quantum mechanics
81Q20 - Semi-classical techniques in quantum theory, including WKB and Maslov methods
81S30 - Phase space methods including Wigner distributions, etc.
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2017 Conference Date : 31/10/2017 Subseries : Research talks arXiv category : Quantum Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:19:41 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-10-31_Mauser.mp4 
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Information on the Event
Event Title : Collisionless Boltzmann (Vlasov) equation and modeling of self-gravitating systems and plasmas / Boltzmann sans collisions, Vlasov et modélisation des systèmes auto-gravitants et des plasmasEvent Organizers : Colombi, Stéphane ; Devriendt, Julien ; Elskens, Yves ; Taruya, Atsushi ; Triay, Roland Dates : 30/10/2017 - 03/11/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1683.html
Citation Data
DOI : 10.24350/CIRM.V.19236603Cite this video as: Mauser, Norbert (2017). The quantum Vlasov equation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19236603 URI : http://dx.doi.org/10.24350/CIRM.V.19236603 |
See Also
- [Multi angle] From Vlasov-Poisson to Euler in the gyrokinetic limit / Author of the conference Miot, Evelyne.
- [Multi angle] 5D full-$f$ gyrokinetic simulation for ion turbulence and transport barrier in tokamak plasmas / Author of the conference Imadera, Kenji.
- [Multi angle] Tracing the dark matter web / Author of the conference Shandarin, Sergei.
- [Post-edited] ColDICE: a parallel Vlasov-Poisson solver using moving adaptative simplicial tessellation / Author of the conference Sousbie, Thierry.
Bibliography
- [1] Bardos, C., & Mauser, N.J. (2017). Équations cinétiques : une histoire française. Gazette des Mathématiciens, to appear -
- [2] Gérard, P., Markowich, P., Mauser, N.J., & Poupaud, F. (1997). Homogenization limits and Wigner transforms. Communications on Pure and Applied Mathematics, 50(4), 323-379 - http://dx.doi.org/10.1002/(SICI)1097-0312(199704)50:4%3C323::AID-CPA4%3E3.0.CO;2-C
- [3] Lions, P.-L., & Paul, T. (1993). Sur les mesures de Wigner. Revista Matemática Iberoamericana, 9(3), 553-618 - http://dx.doi.org/10.4171/RMI/143
- [4] Markowich, P.A., & Mauser, N.J. (1993). The classical limit of a self-consistent quantum Vlasov equation in 3D. Mathematical Models & Methods in Applied Sciences, 3(1), 109-124 - http://dx.doi.org/10.1142/S0218202593000072
- [5] Zhang, P., Zheng, Y., & Mauser, N.J. (2002). The limit from the Schrödinger-Poisson to the Vlasov-Poisson equations with general data in one dimension. Communications on Pure and Applied Mathematics, 55(5), 582-632 - http://dx.doi.org/10.1002/cpa.3017
- [6] Athanassoulis, A.G., Mauser, N.J., & Paul, T. (2009). Coarse-scale representations and smoothed Wigner transforms. Journal de Mathématiques Pures et Appliquées. Neuvième Série, 91(3), 296-338 - http://dx.doi.org/10.1016/j.matpur.2009.01.001
