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Localisation in 1D random random walks

Albert Compte·Jean-Philippe Bouchaud
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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 $\bar{< x^2 > - < x > ^2}$ 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.

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Albert Compte, Jean-Philippe Bouchaud. 1998-01-14. Localisation in 1D random random walks. https://doi.org/10.1088/0305-4470%2F31%2F29%2F004

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