Fluctuations of the probability density of diffusing particles for different realizations of a random medium
- 2 May 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 72 (18) , 2827-2830
- https://doi.org/10.1103/physrevlett.72.2827
Abstract
We study the fluctuations of the probability density P(r,t) of diffusing particles to be at distance r at time t in the presence of random potentials, represented by random transition rates. We find an exact relation which expresses all the moments of P(r,t) in terms of its first moment, for both quenched and annealed disorder and for any dimension. From this relation follows that anomalous diffusion implies nontrivial behavior of the moments of P(r,t), such as an exponential divergence of the relative fluctuations for large r.Keywords
This publication has 29 references indexed in Scilit:
- Multifractality of random walks and localized excitations on linear random fractalsPhysica A: Statistical Mechanics and its Applications, 1992
- Multifractal localizationPhysica A: Statistical Mechanics and its Applications, 1992
- Evidence for superlocalization on a fractal network in conductive carbon-black–polymer compositesPhysical Review Letters, 1992
- Vibrations and random walks on random fractals: Anomalous behaviour and multifractalityPhilosophical Magazine Part B, 1992
- Fractals and Disordered SystemsPublished by Springer Nature ,1991
- Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applicationsPhysics Reports, 1990
- Superlocalization of Electrons and Waves in Fractal MediaEurophysics Letters, 1987
- Diffusion in regular and disordered latticesPhysics Reports, 1987
- Diffusion in disordered mediaAdvances in Physics, 1987
- Excitation dynamics in random one-dimensional systemsReviews of Modern Physics, 1981