Nonlinear stationary solutions of the wigner and wigner-poisson equations

F. Haas, P.K. Shukla

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed
LanguageEnglish
JournalPhysics of Plasmas
Volume15
Issue number11
DOIs
Publication statusPublished - Nov 2008

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Poisson equation
formalism
energy

Keywords

  • Clebsch-Gordan coefficients
  • plasma instability
  • Poisson equation

Cite this

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Nonlinear stationary solutions of the wigner and wigner-poisson equations. / Haas, F.; Shukla, P.K.

In: Physics of Plasmas, Vol. 15, No. 11, 11.2008.

Research output: Contribution to journalArticle

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AU - Shukla, P.K.

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N2 - Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed

AB - Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed

KW - Clebsch-Gordan coefficients

KW - plasma instability

KW - Poisson equation

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DO - 10.1063/1.3008047

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JO - Physics of Plasmas

T2 - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

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