We present a fully nonlinear study of the development of equilibrium after
preheating. Preheating is the exponentially rapid transfer of energy from t
he nearly homogeneous inflaton field to fluctuations of other fields and/or
the inflaton itself. This rapid transfer leaves these fields in a highly n
onthermal state with energy concentrated in infrared modes. We have perform
ed lattice simulations of the evolution of interacting scalar fields during
and after preheating for a variety of inflationary models. We have formula
ted a set of generic rules that govern the thermalization process in all of
these models. Notably, we see that once one of the fields is amplified thr
ough parametric resonance or other mechanisms, it rapidly excites other cou
pled fields to exponentially large occupation numbers. These fields quickly
acquire nearly thermal spectra in the infrared, which gradually propagates
into higher momenta. Prior to the formation of total equilibrium, the exci
ted fields group into subsets with almost identical characteristics (e.g. g
roup effective temperature). The way fields form into these groups and the
properties of the groups depend on the couplings between them. We also stud
ied the onset of chaos after preheating by calculating the Lyapunov exponen
t of the scalar fields.