The dynamics of systems undergoing a second order symmetry breaking phase transition has been studied recently in several instances [@AB; @LZ; @YZ; @ABZ], particularly in association with the theory of topological defect formation [@Kibble; @Zurek] in cosmology [@Book] and in experiments in $^3He$ [@He3] and $^4He$ [@He4]. With experimental data in the pipeline for the collisions of heavy ions at RHIC and later at CERN the effort to identify phase transitions in nuclear matter is also a very active field of research. The Langevin dynamics of effective scalar theories (such as the $\sigma$ model) affords one of the few quantitative windows into such transitions [@BRS].

Theoretically this situation has been modeled by the out-of equilibrium dynamics of a classical scalar field theories (with a given number of flavors) in contact with an external environment at a temperature T, which may be a function of time. The environment is only known statistically and its behavior can then be described in terms of stochastic fields obeying a fluctuation-dissipation relation. The effective evolution of the fields is therefore described by a Langevin field equation.

This stochastic classical description is of course only an approximation to the full quantum evolution. Recently attempts to treat 