Finite temperature simulations from quantum field dynamics?

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