  We describe a Hartree ensemble method to approximately solve the Heisenberg
equations for the \phi^4 model in 1+1 dimensions. We compute the energies and
number densities of the quantum particles described by the \phi field and find
that the particles initially thermalize with a Bose-Einstein distribution for
the particle density. Gradually, however, the distribution changes towards
classical equipartition. Using suitable initial conditions quantum
thermalization is achieved much faster than the onset of this undesirable
equipartition. We also show how the numerical efficiency of our method can be
significantly improved.
