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

TL;DR

This paper analyzes the convergence of the cluster expansion for equal-time Green functions in scalar theories across different dimensions, revealing good convergence in single-phase regions and breakdown in two-phase configurations, with implications for dynamical calculations.

Contribution

It provides a detailed investigation of the convergence properties of the cluster expansion in scalar theories and identifies key timescales affecting adiabaticity in dynamical scenarios.

Findings

Cluster expansion converges well in single-phase regions.

Breaks down in two-phase configurations.

Two timescales govern adiabaticity and tunneling in dynamical calculations.

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.