Diffusion Constant of a Quantum Particle Moving in Tight-Binding Media Modulated by Non-White Noises

Abstract

Diffusion of a particle or an excitation in randomly fluctuating media is studied theoretically. The model is a tight-binding Hamiltonian whose diagonal or off-diagonal elements are modulated by mutually-independent random noises. The non-white modulation models are investigated precisely. The diffusion constant (D) depends on the noise-parameters such as the amplitude (Δ) and the correlation time (γ⁻¹) and also depends on the static band width (W). Explicit calculation of D has been performed by using the dynamical coherent potential approximation and by computer experiments. In the case that diagonal elements are modulated by discrete-jump noises, D as a function of γ has a minimum in the vicinity of hγ=Δ if Δ>>W. On the contrary, D(γ) is a monotonically-increasing function of γ if Δ<<W. In the off-diagonal fluctuation case, the diffusion constant exhibits a feature qualitatively different from the diagonal fluctuation model.