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

The path integral method is applied to the study of a stochastic Hamiltonian describing the motion of a quasiparticle in a dynamically fluctuating medium. Formulas to calculate the density of states and the diffusion constant of the quasiparticle are derived on the basis of the path integral method, which enables us to compute their exact values numerically for arbitrary fluctuations. Numerical calculation is demonstrated for one-dimensional systems with site-energy fluctuations obeying an asymmetric two-state-jump Markoff process. As far as one-particle quantities, such as the density of states, are concerned, no marked discrepancy between our results and those of the coherent potential approximation are observed. As for the diffusion constant, on the other hand, the two results exhibit qualitatively different behavior which is related to the localization of a quasiparticle, particularly for slow fluctuations.