Numerical analysis of diffusion of a quasiparticle in a dynamically fluctuating medium based on the path integral method II

A numerical study of the density of states and the diffusion constant is developed based on the path integral method for a stochastic Hamiltonian describing the motion of a quasiparticle in a dynamically fluctuating medium. A general stochastic process consisting of an arbitrary number of asymmetric two-state-jump Markoff processes is introduced to describe the site-energy fluctuations. This general process enables us to make an interpolation between a single two-state-jump Markoff process and a Gaussian Markoff process and also describe the intermediate process. Transient behavior of the density of states and the diffusion constant is observed for slow fluctuations as N changes from one to infinity, where N is the number of the constituent two-state-jump Markoff process. Effects of the asymmetric distribution, which may be ascribed to the temperature of the fluctuating medium, on the diffusion constant have also been clarified for several values of N. The results of the CPA and those of the perturbational method are compared with our results.