  We investigate the quantum Vlasov equation with a source term describing the
spontaneous particle creation in strong fields. The back-reaction problem is
treated by solving this kinetic equation together with the Maxwell equation
which determines the induced time-dependent electric field in the system. The
evolution of distribution functions for bosons and fermions is studied
numerically. We found that the system shows a regular dynamic behavior if the
back-reaction is neglected. But if the back-reaction is included, it is not the
case and some stochastic features are clearly revealed in the non-equilibrium
distribution function..
