Convergence properties of the cluster expansion for equal-time Green functions in scalar theories

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.