We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period pl . Allowing for collisions, these oscillations are damped on a time scale r determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless r ӷ pl and pl ϳ1/⌳ QCD ϳ1 fm/c. ͓S0556-2821͑99͒06123-8͔

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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.

Dynamics of partons created through vacuum tunneling in time-dependent spatially homogeneous field is studied for typical conditions of ultra-relativistic heavy-ion collisions. In the relaxation-time approximation, a thermalization scenario for such quasi-particle plasma is considered. A local equilibrium state of the system is described in the framework of two-component thermodynamics of particles and anti-particles. In the evolution towards an equilibrium are involved three parallel mechanisms: (i) spontaneous vacuum pair creation, (ii) back-reaction of the produced particles to the background field, (iii) collisions between the charged particles. We solve numerically a self-consistent system of the Vlasov-like kinetic equation with a source and collision term and the renormalized Maxwell equation. A possibility of introducing the temperature conception under the condition of strong vacuum polarization is discussed.