models considered here [@BW] and seemingly result from the truncation of the system at any finite order in a hierarchy of correlators. The overdamped limit, $k^2 + m^2 + \Delta m^2(t) << \eta$ is obtained when $C_k^2 \simeq A_k^2/\eta << B_k^2, A_k^2$.

Again we see that the effort in solving the mean-field second order Fokker-Plank equation is comparable to its Langevin counterpart, but with the stochastic averages taken into account. A renormalization scheme for rendering these equations ultraviolet cutoff independent can be constructed, if desired, following standard techniques for mean-field evolutions [@Cooper].

The uses of the closed form solutions of the Fokker-Planck equation {#Dyn}
===================================================================

The solutions presented above permit some analysis of several important dynamical situations.

In many cases in field theory the harmonic solutions can reveal the essential physics of the (short time) evolution. This is true for example for the motion of soft fields in the vicinity of a second order phase transition, where only the lowest relevant operators are needed, and for some situations when (spinodal) instabilities can develop, such as in the early stages of reheating after cosmological inflation or in the aftermath of a violent pressure quench, in some condensed matter experiments.

In this 