RANDOM-WALK ON A LINEAR-CHAIN WITH A QUENCHED DISTRIBUTION OF JUMP LENGTHS

We study the random walk of a particle on a linear chain, where a jump length 1 or 2 is assigned randomly to each lattice site with probabil ity p(1) and p(2) = 1-p(1), respectively. We find that the probability p(1)(eff) for the particle to be at a site with jump length 1 is diff erent from p(1), which causes the diffusion coefficient D to differ fr om the mean-field result. A theory is developed that allows us to calc ulate p(1)(eff) and D for all values of p(1). In the limit p(1)-->0, t he theory yields a nonanalytic dependence of p(1)(eff) on p(1)(eff)sim ilar to - p(1)(2)lnp(1).