Quantum dynamics of phase transitions in broken symmetry lf field theory

We perform a detailed numerical investigation of the dynamics of a single component ‘‘explicitly broken symmetry’’ lf field theory in 111 dimensions, using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation ~BVA!. We assume here that the initial state is described by a Gaussian density matrix peaked around some nonzero value of ^f(0)&, and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: the Hartree approximation, the BVA, and a related two-particle irreducible ~2PI! 1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits behavior consistent with a second order phase transition. We find that the average fields equilibrate for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how ^f(t)& and ^x(t)& depend on the initial temperature and on the coupling constant. The Fourier transform of the two-point functions at late times can be fitted by a Bose-Einstein distribution function whose temperature is independent of momentum. We interpret this as evidence for thermalization.