Spatial correlations of random potentials and the dynamics of quantum coherence

Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].