  We investigate the convergence properties of the cluster expansion of
equal-time Green functions in scalar theories with quartic self-coupling in
(0+1), (1+1), and (2+1) space-time dimensions. The computations are carried out
within the equal-time correlation dynamics approach. We find that the cluster
expansion shows good convergence as long as the system is in a single phase
configuration and that it breaks down in a two phase configuration, as one
would naively expect. In the case of dynamical calculations with a time
dependent Hamiltonian we find two timescales determining the adiabaticity of
the propagation; these are the time required for adiabaticity in the single
phase region and the time required for tunneling into the non-localized lowest
energy state in the two phase region.
