Localisation in 1D random random walks

Abstract

Diffusion in a one dimensional random force field leads to interesting localisation effects, which we study using the equivalence with a directed walk model with traps. We show that although the average dispersion of positions $\overline{<x^2>-<x{>}^2}$ diverges for long times, the probability that two particles occupy the same site tends to a finite constant in the small bias phase of the model. Interestingly, the long time properties of this off-equilibrium, aging phase is similar to the equilibrium phase of the Random Energy Model.

submitted to J. Phys. A

References in corpus (1)

• Universality Classes for Extreme Value Statistics

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