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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 1, Pages 109–125 (Mi tvp149)  

This article is cited in 10 scientific papers (total in 10 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

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English version:
Theory of Probability and its Applications, 2007, 51:1, 168–181

Bibliographic databases:

Document Type: Article
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
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    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:
    1. Kozlov V.V., Smolyanov O.G., “The relativistic Poincaré model”, Dokl. Math., 80:2 (2009), 769–774  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Kupsch J., Smolyanov O.G., “Generalized Wiener-Segal-Fock representations and Feynman formulae”, Dokl. Math., 79:2 (2009), 153–157  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Kozlov V.V., Smolyanov O.G., “Infinite-dimensional equation Liouville with respect to measures”, Dokl. Math., 81:3 (2010), 476–480  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. 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  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. 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  crossref  mathscinet  zmath  isi  elib  scopus
    7. Burkatskii M.O., “Feynman Approximations of the Dynamics of the Wigner Function”, Russ. J. Math. Phys., 22:4 (2015), 454–462  crossref  mathscinet  zmath  isi  scopus
    8. 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  crossref  adsnasa  isi  elib  scopus
    9. Gough J., Ratiu T.S., Smolyanov O.G., “Wigner Measures and Quantum Control”, Dokl. Math., 91:2 (2015), 199–203  crossref  mathscinet  zmath  isi  elib  scopus
    10. Ratiu T.S., Smolyanov O.G., “Wigner Quantization of Hamilton-Dirac Systems”, Dokl. Math., 91:1 (2015), 114–116  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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