  We study the real-time evolution of a self-interacting O(N) scalar field
initially prepared in a pure quantum state. We present a complete solution of
the nonequilibrium quantum dynamics from a 1/N-expansion of the
two-particle-irreducible effective action at next-to-leading order, which
includes scattering and memory effects. Restricting one's attention (or ability
to measure) to a subset of the infinite hierarchy of correlation functions, the
system is described by an effective (reduced) density matrix which, unlike the
full density matrix, has a nontrivial time evolution. In particular, starting
from a pure quantum state, we observe the loss of putity/coherence and, on
longer time scales, thermalization of the reduced density matrix. We point out
that the physics of decoherence is well described by classical statistical
field theory.
