  We consider the out-of-equilibrium evolution of a classical condensate field
and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a
symmetric and a double well potential. We use the 2PPI formalism and go beyond
the Hartree approximation by including the sunset term. In addition to the mean
field phi=<Phi> the 2PPI formalism uses as variational parameter a time
dependent mass M**2(t) which contains all local insertions into the Green
function. We compare our results to those obtained in the Hartree
approximation. In the symmetric Phi**4 theory we observe that the mean field
shows a stronger dissipation than the one found in the Hartree approximation.
The dissipation is roughly exponential in an intermediate time region. In the
theory with spontaneous symmetry breaking, i.e., with a double well potential,
the field amplitude tends to zero, i.e., to the symmetric configuration. This
is expected on general grounds: in 1+1 dimensional quantum field theory there
is no spontaneous symmetry breaking for T >0, and so there should be none at
finite energy density (microcanonical ensemble), either. Within the time range
of our simulations the momentum spectra do not thermalize and display
parametric resonance bands.
