  A charged parallel plate capacitor will create particle-antiparticle pairs by
the Schwinger process and discharge over time. We consider the full quantum
discharge process in 1+1 dimensions including backreaction, when the electric
field interacts with massless charged fermions. We recover oscillatory features
in the electric field observed in a semiclassical analysis and find that the
amplitude of the oscillations falls off as t^{-1/2} and that stronger coupling
implies slower decay. Remarkably, Ohm's law applies to the vacuum and we
evaluate the quantum electrical conductivity of the vacuum to be e/\pi^{1/2},
where e is the fermionic charge. Similarities and differences with black hole
evaporation are mentioned.
