LOCALIZATION IN ONE-DIMENSIONAL RANDOM RANDOM-WALKS

Diffusion in a one-dimensional random force field leads to interesting localization effects, which we study using the equivalence with a dir ected walk model with traps. We show that although the average dispers ion of positions <([x(2)] - [x](2))over bar> diverges for long times, the probability that two independent particles occupy the same site te nds to a finite constant in the small bias phase of the model. Interes tingly, the long-time properties of this off-equilibrium, ageing phase is similar to the equilibrium phase of the random energy model.