Localization in one-dimensional random random walks
- 24 July 1998
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 31 (29) , 6113-6121
- https://doi.org/10.1088/0305-4470/31/29/004
Abstract
Diffusion in a one-dimensional random force field leads to interesting localization effects, which we study using the equivalence with a directed walk model with traps. We show that although the average dispersion of positions diverges for long times, the probability that two independent 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, ageing phase is similar to the equilibrium phase of the random energy model.Keywords
All Related Versions
This publication has 18 references indexed in Scilit:
- Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applicationsPhysics Reports, 1990
- Classical diffusion of a particle in a one-dimensional random force fieldAnnals of Physics, 1990
- A comparison of the error function and the tanh transformation as progressive rules for double and triple singular integralsJournal of Computational and Applied Mathematics, 1990
- Dynamical exponents for one-dimensional random-random directed walksJournal of Statistical Physics, 1990
- Diffusion anormale dans les milieux désordonnés : piégeage, corrélations et théorèmes de la limite centraleJournal de Physique, 1987
- Localization of random walks in one-dimensional random environmentsCommunications in Mathematical Physics, 1984
- The simplest spin glassNuclear Physics B, 1984
- Classical Diffusion on a Random ChainPhysical Review Letters, 1982
- Random-energy model: An exactly solvable model of disordered systemsPhysical Review B, 1981
- Random-Energy Model: Limit of a Family of Disordered ModelsPhysical Review Letters, 1980