Diffusion on Percolation Clusters
Diffusion on percolating clusters has attracted much attention since de Gentles´ proposal1 of the “ant in the labyrinth”. It has recently been realized2 that diffusion becomes anomalous for times shorter than a typical crossover time, τ, of order ξ2+θ where e—ξ~|p c-p|-v is the percolation correlation length and θ describes the scaling of the diffusion coefficent on the infinite percolating cluster above the threshold p c, D~ξ-θ . On the infinite cluster, the mean square distance <r 2> after t time steps behaves as t 2/(2+ θ ) for 1«t«τ, and as Dt for t»τ. τ is thus the time it takes to diffuse a typical distance ξ. Similar anomalous diffusion occurs on finite clusters, for distances short compared to the cluster size.
KeywordsAmplitude Ratio Percolation Cluster Cayley Tree Diffusion Coefficent Infinite Cluster
Unable to display preview. Download preview PDF.
- 1.P. G. de Gennes, La Recherche 7, 919 (1976).Google Scholar
- 3.A. B. Harris, Y. Meir and A. Aharony, Phys. Rev. B (submitted).Google Scholar
- 4.C. D. Mitescu and J. Russeng, Ann. Israel. Phys. Soc. 5, 81 (1983).Google Scholar
- 6.e.g. D. Stauffer, Introduction to Percolation Theory ( Taylor and Francis, London 1985 ).Google Scholar
- 9.Y. Meir, J. Phys. A Lett. (in press).Google Scholar