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For homogeneous initial conditions, Hartree (gaussian) dynamicalapproximations are known to have problems with thermalization, because ofinsufficient scattering. We attempt to improve on this by writing an arbitrarydensity matrix as a superposition of gaussian pure states and applying theHartree approximation to each member of such an ensemble. Particles can thenscatter via their back-reaction on the typically inhomogeneous mean fields.Starting from initial states which are far from equilibrium we numericallycompute the time evolution of particle distribution functions and observe thatthey indeed display approximate thermalization on intermediate time scales byapproaching a Bose-Einstein form. However, for very large times thedistributions drift towards classical-like equipartition.Comment: 30 pages revtex including figures. Added clarification

Thermalization in a Hartree ensemble approximation to quantum field dynamics