Classical Diffusion in One-Dimensional Disordered Lattice

Classical diffusion of localized excitations is investigated on a one-dimensional chain with (energy-independent) nearest-neighbor transfer rates Wn,n+1=Wn+1,n that are independently distributed according to a probability density ρ(W). An exact formal solution is derived for 〈P₀(t)〉, the time development of the initial excitation. The long-time decay of 〈P₀(t)〉, determined by the behavior of ρ(W) near $W=0$, is analyzed in detail for arbitrary probability densities ρ(W).