|
This article is cited in 12 scientific papers (total in 12 papers)
Wigner function and diffusion in collisionfree media of quantum particles
V. V. Kozlova, O. G. Smolyanovb a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
A quantum Poincaré model (realizing behavior of ideal gas of noninteracting quantum Bolztman particles) is introduced. We use the fact that the evolution of the Wigner function corresponding to a quantum system with a quadratic Hamiltonian coincides with the evolution of a probability distribution on a phase space of the Hamiltonian system, the quantization of which gives the quantum system under consideration.
Keywords:
Poincaré model, Wigner function, Heisenberg equation, Hamiltonian equation, Weyl operator, Weyl function, ideal gas.
DOI:
https://doi.org/10.4213/tvp149
Full text:
PDF file (2176 kB)
References:
PDF file
HTML file
English version:
Theory of Probability and its Applications, 2007, 51:1, 168–181
Bibliographic databases:
Received: 06.10.2005
Citation:
V. V. Kozlov, O. G. Smolyanov, “Wigner function and diffusion in collisionfree media of quantum particles”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 109–125; Theory Probab. Appl., 51:1 (2007), 168–181
Citation in format AMSBIB
\Bibitem{KozSmo06}
\by V.~V.~Kozlov, O.~G.~Smolyanov
\paper Wigner function and diffusion in collisionfree media of quantum particles
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 1
\pages 109--125
\mathnet{http://mi.mathnet.ru/tvp149}
\crossref{https://doi.org/10.4213/tvp149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2324169}
\zmath{https://zbmath.org/?q=an:1120.82005}
\elib{https://elibrary.ru/item.asp?id=9233592}
\transl
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 1
\pages 168--181
\crossref{https://doi.org/10.1137/S0040585X97982220}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000245677000010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247522216}
Linking options:
http://mi.mathnet.ru/eng/tvp149https://doi.org/10.4213/tvp149 http://mi.mathnet.ru/eng/tvp/v51/i1/p109
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
Kozlov V.V., Smolyanov O.G., “The relativistic Poincaré model”, Dokl. Math., 80:2 (2009), 769–774
-
Kupsch J., Smolyanov O.G., “Generalized Wiener-Segal-Fock representations and Feynman formulae”, Dokl. Math., 79:2 (2009), 153–157
-
Kozlov V.V., Smolyanov O.G., “Infinite-dimensional equation Liouville with respect to measures”, Dokl. Math., 81:3 (2010), 476–480
-
Kozlov V.V., Smolyanov O.G., “Wigner measures on infinite-dimensional spaces and the Bogolyubov equations for quantum systems”, Dokl. Math., 84:1 (2011), 571–575
-
I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78
-
Gough J., Ratiu T.S., Smolyanov O.G., “Feynman, Wigner, and Hamiltonian Structures Describing the Dynamics of Open Quantum Systems”, Dokl. Math., 89:1 (2014), 68–71
-
Burkatskii M.O., “Feynman Approximations of the Dynamics of the Wigner Function”, Russ. J. Math. Phys., 22:4 (2015), 454–462
-
Zare S., Rezaee S., Yazdani E., Anvari A., Sadighi-Bonabi R., “Relativistic Gaussian Laser Beam Self-Focusing in Collisional Quantum Plasmas”, Laser Part. Beams, 33:3 (2015), 397–403
-
Gough J., Ratiu T.S., Smolyanov O.G., “Wigner Measures and Quantum Control”, Dokl. Math., 91:2 (2015), 199–203
-
Ratiu T.S., Smolyanov O.G., “Wigner Quantization of Hamilton-Dirac Systems”, Dokl. Math., 91:1 (2015), 114–116
-
Burkatckii M.O., “Wigner Function of Open Quantum System”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:4 (2018), 1850026
-
A. I. Komech, E. A. Kopylova, “Attractors of nonlinear Hamiltonian partial differential equations”, Russian Math. Surveys, 75:1 (2020), 1–87
|
Number of views: |
This page: | 663 | Full text: | 114 | References: | 100 |
|