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

Abstract

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.

19 pages, 5 postscript figures

References in corpus (3)

• Vibrations versus collisions and the iterative structure of two-body dynamics
• Connected Green function approach to ground state symmetry breaking in ${\Phi }_{1+1}^4$-theory
• Constraint Correlation Dynamics of SU(N) Gauge Theories

Cited by in corpus (4)

• From Kadanoff-Baym dynamics to off-shell parton transport
• Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory
• Nonequilibrium Quantum-Field Dynamics and Off-Shell Transport for ${\varphi }^4$-theory in 2+1 dimensions
• Convergence properties of the equal-time connected Green function approach for temporal gauge SU(2)_{2+1} Yang-Mills theory