  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.
