Non-Equilibrium Real-Time Dynamics of Quantum Fields: Linear and   Non-Linear Relaxation in Scalar and Gauge Theories
  The real time evolution of field condensates is solved for small and large field amplitudes in scalar theories.For small amplitudes,the quantum equations of motion for the condensate can be linearized and solved by Laplace transform. The late time evolution turns to be determined by the singularities in the complex plane (one-particle poles, two- and multi- particle cuts, Landau cuts for non-zero initial temperature). In hot scalar electrodynamics, we solve the real time evolution of field condensates with soft length scales \sim k^{-1}>(eT)^{-1}. Transverse gauge invariant condensates relax as 1/t^2 to amplitudes determined by the quasiparticle poles. We rederive the HTL action using the non-equilibrium field theory techniques.In the nonlinear regime (for large initial energy densities) we analyze the dynamics of dissipation and relaxation in scalar theory after linear unstabilities are shut-off by the quantum back-reaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non-perturbative in the coupling and initial amplitude. A combination of numerical analysis and the implementation of a dynamical renormalization group resummation via multi-time scale analysis reveals the presence of unstable bands in the nonlinear regime. These are associated with power law growth of quantum fluctuations, that result in power law relaxation and dissipation with {\bf non-universal and non-perturbative dynamical anomalous exponents. 
D. Boyanovsky, H. J. de Vega, R. Holman, S. Prem Kumar, Rob D.   Pisarski and J. Salgado