Exact solution of the Hu-Paz-Zhang master equation - art. no. 105020

The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillat or and bath are initially uncoupled. Here an exact general solution is obta ined in the form of an expression for the Wigner function at time t in term s of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is f ound to be due to the zero-point oscillations of the bath and not removed i n a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillati ons are neglected. In that limit closed form expressions for wave packet sp reading and attenuation of coherence are obtained. These results agree with in a numerical factor with those appearing in the literature, which apply f or the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obt ained for the physically consistent case in which the initial particle temp erature is arranged to coincide with that of the bath.