Explicit Solution of the Time Evolution of the Wigner Function

Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of motion. They can be solved easily and their solutions can be utilized to construct the time evolution of the Wigner function. In this paper, the usefulness of this explicit solution is demonstrated by solving a numerical example in which the Wigner function has strong spatial and temporal variations as well as regions with negative values. It is found that the explicit solution gives a correct description of the time evolution of the Wigner function. We examine next the pseudoparticle approximation which uses classical trajectories to evolve the Wigner function. We find that the pseudoparticle approximation reproduces the general features of the time evolution, but there are deviations. We show how these deviations can be systematically reduced by including higher-order correction terms in powers of $\hbar^2$.Comment: 16 pages, in LaTex, invited talk presented at the Wigner Centennial Conference, Pecs, Hungary, July 8-12, 2002, to be published in the Journal of Optics B: Quantum and Classical Optics, June 200

Nonlinear effects in tunnelling escape in N-body quantum systems

We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum equations of the multiparticle system we find the tunneling rate and time evolutions of the number of trapped particles for different nonlinearity values.Comment: 10 pages, 3 figure

Generalized gradient expansions in quantum transport equations

Gradient expansions in quantum transport equations of a Kadanoff-Baym form have been reexamined. We have realized that in a consistent approach the expansion should be performed also inside of the self-energy in the scattering integrals of these equations. In the first perturbation order this internal expansion gives new correction terms to the generalized Boltzman equation. These correction terms are found here for several typical systems. Possible corrections to the theory of a linear response to weak electric fields are also discussed.Comment: 20 pages, latex, to appear in Journal of Statistical Physics, March (1997