 
Summary: Exact and truncated dynamics in nonequilibrium field theory
Gert Aarts, Gian Franco Bonini, and Christof Wetterich
Institut fušr Theoretische Physik, Universitašt Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Received 2 August 2000; published 21 December 2000
Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of
a hierarchy of correlation functions, using approximation methods such as Hartree, large Nf , and nPIeffective
action techniques. These truncation schemes can be implemented equally well in a classical statistical system,
where results can be tested by comparison with the complete nonlinear evolution obtained by numerical
methods. For a (1 1)dimensional scalar field we find that the earlytime behavior is reproduced qualitatively
by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show
that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the
fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly
on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the
fixed point, the full nonlinear evolution shows thermalization with a surprisingly slow relaxation.
DOI: 10.1103/PhysRevD.63.025012 PACS number s : 11.15.Kc, 05.70.Ln, 11.10.Kk, 11.10.Wx
I. INTRODUCTION
An understanding of the dynamical evolution of nonequi
librium quantum fields is needed in diverse physical situa
tions as nonrelativistic condensed matter, relativistic heavy
ion colliders, and the early universe. For several reasons a
