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

This article is cited in 14 scientific papers (total in 14 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

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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
\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
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 1
\pages 168--181

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    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
    11. Burkatckii M.O., “Wigner Function of Open Quantum System”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:4 (2018), 1850026  crossref  mathscinet  zmath  isi  scopus
    12. A. I. Komech, E. A. Kopylova, “Attractors of nonlinear Hamiltonian partial differential equations”, Russian Math. Surveys, 75:1 (2020), 1–87  mathnet  crossref  crossref  mathscinet  isi  elib
    13. Burkatskii M.O., “Reduced Dynamics of the Wigner Function”, Russ. J. Math. Phys., 27:1 (2020), 18–21  crossref  mathscinet  isi
    14. J. E. Gough, T. S. Ratiu, O. G. Smolyanov, “Wigner Measures and Coherent Quantum Control”, Proc. Steklov Inst. Math., 313 (2021), 52–59  mathnet  crossref  crossref  isi  elib
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