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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
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http://mi.mathnet.ru/eng/tvp149https://doi.org/10.4213/tvp149 http://mi.mathnet.ru/eng/tvp/v51/i1/p109
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This publication is cited in the following articles:
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Kozlov V.V., Smolyanov O.G., “The relativistic Poincaré model”, Dokl. Math., 80:2 (2009), 769–774
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Kupsch J., Smolyanov O.G., “Generalized Wiener-Segal-Fock representations and Feynman formulae”, Dokl. Math., 79:2 (2009), 153–157
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Kozlov V.V., Smolyanov O.G., “Infinite-dimensional equation Liouville with respect to measures”, Dokl. Math., 81:3 (2010), 476–480
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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
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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
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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
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Burkatskii M.O., “Feynman Approximations of the Dynamics of the Wigner Function”, Russ. J. Math. Phys., 22:4 (2015), 454–462
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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
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Gough J., Ratiu T.S., Smolyanov O.G., “Wigner Measures and Quantum Control”, Dokl. Math., 91:2 (2015), 199–203
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Ratiu T.S., Smolyanov O.G., “Wigner Quantization of Hamilton-Dirac Systems”, Dokl. Math., 91:1 (2015), 114–116
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Burkatckii M.O., “Wigner Function of Open Quantum System”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:4 (2018), 1850026
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A. I. Komech, E. A. Kopylova, “Attractors of nonlinear Hamiltonian partial differential equations”, Russian Math. Surveys, 75:1 (2020), 1–87
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Burkatskii M.O., “Reduced Dynamics of the Wigner Function”, Russ. J. Math. Phys., 27:1 (2020), 18–21
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J. E. Gough, T. S. Ratiu, O. G. Smolyanov, “Wigner Measures and Coherent Quantum Control”, Proc. Steklov Inst. Math., 313 (2021), 52–59
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