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

A numerical study is developed on the motion of a quasiparticle in a dynamically fluctuating medium based on the path integral method. The diffusion constant of the quasiparticle is calculated for one-dimensional systems with both site-energy (diagonal) and transfer-energy (off-diagonal) fluctuations obeying a general stochastic process, which is a superposition of an arbitrary number of two-state-jump Markoff processes with asymmetric probability distribution of stochastic variables. This general stochastic process enables us to link a two-state-jump Markoff process and a Gaussian Markoff process and describe the intermediate process. Effects of the asymmetric distribution on the diffusion constant is also clarified. It is found that off-diagonal fluctuations bring qualitatively different effects on the diffusion of the quasiparticle compared with the diagonal fluctuation case; for example, the diffusion constant has minima as a function of the amplitude of fluctuating transfer energy and has a minimum as a function of the asymmetry parameter. Adding diagonal fluctuations, the former minimum remains, whereas the latter minimum disappears for off-diagonal fluctuations consisting of a single two-state-jump Markoff process. This behavior of the diffusion constant strongly depends on N1, the number of the constituent two-state-jump Markoff process.