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We investigate the quantum Vlasov equation with a source term describing thespontaneous particle creation in strong fields. The back-reaction problem istreated by solving this kinetic equation together with the Maxwell equationwhich determines the induced time-dependent electric field in the system. Theevolution of distribution functions for bosons and fermions is studiednumerically. We found that the system shows a regular dynamic behavior if theback-reaction is neglected. But if the back-reaction is included, it is not thecase and some stochastic features are clearly revealed in the non-equilibriumdistribution function..Comment: 7 pages, LaTeX, 9 figures, sprocl.sty, psfig.sty, talk presented at  the Workshop "Kadanoff-Baym Equations - Progress and Perspectives for  Many-Body Physics", September 20-24, 1999, Rostock University; some changes  in abstract, extended introduction, references adde

THE NON-EQUILIBRIUM DISTRIBUTION FUNCTION OF PARTICLES AND ANTI-PARTICLES CREATED IN STRONG FIELDS