Influence of coloured noise on the diffusion of a quantum particle. Part II: Diffusion constant for dichotomic markovian fluctuations

In part I of this paper a new formalism for the calculation of stochastic moments in quantum mechanical particle motion has been developed. Now we use this formalism to obtain expressions for the mean square displacement within a model containing dichotomic Markovian fluctuations. A self-energy like quantity in the equation of motion for a contracted kernel or propagator determining the mean square displacement is replaced by its second order approximation in powers of the deterministic part of the Hamiltonian. This is the only approximation throughout the paper. In the one-dimensional case the contracted propagator itself is calculated. Instead, in the general case the mean square displacement is given in terms of a continued fraction. We compare our result to several previous ones and especially discuss the question of Anderson, localization in the static limit.