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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

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

This article is cited in 15 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.

Received: 06.10.2005

DOI: 10.4213/tvp149


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

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