Non-Equilibrium Dynamics of a Quench-Induced Phase Transition and   Topological Defect Formation
  We study the full out-of-thermal-equilibrium dynamics of a relativistic classical scalar field through a symmetry breaking phase transition. In these circumstances we determine the evolution of the ensemble averages of the correlation length and topological defect densities. This clarifies many aspects of the non-perturbative dynamics of fields in symmetry breaking phase transitions and allows us to comment on a quantitative basis on the canonical pictures for topological defect formation and evolution. We also compare these results to those obtained from the field evolution in the Hartree approximation or using the linearized theory. By doing so we conclude about the regimes of validity of these approximations. 
N. D. Antunes and L. M. A. Bettencourt