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In this paper we study the quantum corrections to the Bernstein-Greene-Kruskal equilibria of plasma physics by using perturbation methods near the classical solution. We obtain the solution for the Wigner function and for the self-consistent potential to first order in the smallness parameter, which is the square of Planck's constant (in dimensionless form), and investigate the structure of the quantum phase space. [ABSTRACT FROM AUTHOR]

In this work, the long-time behavior of the solutions of the Vlasov-Poisson system when starting near a spatially homogeneous equilibrium is analyzed numerically. It is found that the asymptotic state toward which the system evolves is not a Bernstein-Green-Kruskal (BGK) equilibrium, but can rather be described by a superposition of BGK modes. Also, it is shown that the small oscillations at the plasma frequency after saturation in the one-sided bump-ontail instability are due to beating between the unstable mode and the least stable mode. [ABSTRACT FROM AUTHOR]