  We study the behavior of out of equilibrium retarded, advanced and correlated
Green's functions within the context of an exactly soluble (quenched) model. We
show, to the lowest order, that even though the pinch singularities cancel,
there is a residual linear dependence on the time interval (after the quench)
in the correlated Green's function which may invalidate perturbation theory. We
sum the perturbation series to all orders in this simple model and show
explicitly that the complete Green's functions are well behaved even for large
time intervals. The exact form of the correlated Green's function allows us to
extract a manifestly positive distribution function, for large times after the
quench, which has a memory of the frequency of the initial system before the
quench.
