Physical Review Letters · 1982 · 180 citations · 6 references
EngineeringPhysicsProbability TheoryStochastic ProcessesTransport PhenomenaBrownian MotionDiffusion ProcessesMarkov ChainsMarkov ProcessesStatistical MechanicsTime-dependent TransportDiffusionsHopping DynamicsKinetic Transport EquationsTime-dependent Diffusion
A simple model of classical diffusion on a random chain is studied. The velocities to the right and to the left are calculated. When one changes continuously the probability distribution $\ensuremath{\rho}$ of the hopping rates, a whole region is found where these two velocities vanish. In this region, the distance $R$ covered by a particle during the time $t$ behaves like $R\ensuremath{\sim}{t}^{x}$, where $x$ depends continuously on $\ensuremath{\rho}$. The exponent $x$ is calculated for a simple example.
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Excitation dynamics in random one-dimensional systems
S. Alexander, J. Bernasconi, W. R. Schneider et al. · Reviews of Modern Physics · 1981 · 756 citations
Random Walks in a Random Environment
Fred Solomon · The Annals of Probability · 1975 · 548 citations · Full text