Pair creation: Back reactions and damping

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 ${\tau }_{\mathrm{pl}}.$ Allowing for collisions, these oscillations are damped on a time scale ${\tau }_r$ determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless ${\tau }_r\gg {\tau }_{\mathrm{pl}}$ and ${\tau }_{\mathrm{pl}}\sim 1/{\Lambda }_{\mathrm{QCD}}\sim 1$ fm/c.