Variable range random walk

Exploiting the coherent medium approximation, I investigate a random walk on objects distributed randomly in a continuous space when the jump rate depends on the distance between two adjacent objects. In one dimension, it is shown that when the jump rate decays exponentially in the long distance limit, a non-diffusive to diffusive transition occurs as the density of sites is increased. In three dimensions, the transition exists when the jump rate has a super Gaussian decay.