John F. Dawson

Quantum dynamics of phase transitions in broken symmetry lambda phi**4 field theory

We perform a detailed numerical investigation of the dynamics of broken symmetry

CHAOS IN TIME-DEPENDENT VARIATIONAL APPROXIMATIONS TO QUANTUM DYNAMICS

\lambda \phi^4

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of {lambda}{phi}{sup 4} field theory

field theory in 1+1 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 the initial state is described by a Gaussian density matrix peaked around some non-zero value of

Renormalized broken-symmetry Schwinger-Dyson equations and the two-particle irreducible 1 / N expansion for the O ( N ) model

, 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: Hartree, BVA and a related 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 a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how

Nonperturbative Predictions for Cold Atom Bose Gases with Tunable Interactions

and

Electric field induced domains in twisted nematic liquid crystals

depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for