Existence, uniqueness and asymptotic behavior of Wigner-Poisson and Vlasov-Poisson systems: A survey
作者:
R. Diner,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 1997)
卷期:
Volume 26,
issue 1-2
页码: 195-207
ISSN:0041-1450
年代: 1997
DOI:10.1080/00411459708221783
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
We present a review of the Wigner-Poisson system of equations, including its equivalence to a Schrödinger-Poisson system when such an equivalence exists, and including its relationship to the Vlasov equation in the classical limith→ 0. Existence and uniqueness for a particle cloud in all space, in a periodic setting, and with a nonlinear Poisson equation and periodic boundary conditions are all discussed. Finally, some results on asymptotic decay of solutions are mentioned for both the Wigner-Poisson system and the Vlasov-Poisson system in the repulsive case. These results are founded on an identity known in the quantum context as “pseudo-conformal conservation law”. The counterparts of this identity for the Vlasov-Poisson system and the classicalN—body problem are presented.
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