Controlled nonperturbative dynamics of quantum fields out of equilibrium

We compute the nonequilibrium real-time evolution of an O (N)-symmetric scalar quantum field theory from a systematic I IN expansion of the 2PI effective action to next-to-leading order, which includes scattering and memory effects. In contrast to the standard 1/N expansion of the 1PI effective action, the next-to-leading-order expansion in presence of a possible expectation value for the composite operator leads to a bounded-time evolution where the truncation error may be controlled by higher powers in I IN. We present a detailed comparison with the leading-order results and determine the range of validity of standard mean-fleld-type approximations We investigate "quench" and "tsunami" initial conditions frequently used to mimic idealized far-from-equilibrium pion dynamics in the context of heavy-ion collisions. For spatially homogeneous initial conditions, we find three generic regimes, characterized by an early-time exponential damping, a parametrically slow (power-law) behavior at intermediate times, and a late-time exponential approach to thermal equilibrium. The different time scales are obtained, from a numerical solution of the time-reversal invariant equations in 1 + 1 dimensions without further approximations. We discuss in detail the out-of-equilibrium behavior of the nontrivial n-point correlation functions as well as the: evolution of a particle number distribution and inverse slope parameter. (C) 2002 Elsevier Science B.V. All rights reserved.