Diffusion on Percolation Clusters

  • Yigal Meir
  • A. Brooks Harris
  • Amnon Aharony
Part of the NATO ASI Series book series (volume 167)


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-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.


Amplitude Ratio Percolation Cluster Cayley Tree Diffusion Coefficent Infinite Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. G. de Gennes, La Recherche 7, 919 (1976).Google Scholar
  2. 2.
    Y. Gefen, A. Aharony and S. Alexander, Phys. Rev. Lett. 50, 77 (1983).ADSCrossRefGoogle Scholar
  3. 3.
    A. B. Harris, Y. Meir and A. Aharony, Phys. Rev. B (submitted).Google Scholar
  4. 4.
    C. D. Mitescu and J. Russeng, Ann. Israel. Phys. Soc. 5, 81 (1983).Google Scholar
  5. 5.
    R. Fisch and A. B. Harris, Phys. Rev. B 18, 416 (1983).ADSCrossRefGoogle Scholar
  6. 6.
    e.g. D. Stauffer, Introduction to Percolation Theory ( Taylor and Francis, London 1985 ).Google Scholar
  7. 7.
    J. Adler, A. Aharony, Y. Meir and A. B. Harris, J. Phys. A 19, 3631 (1986).ADSCrossRefGoogle Scholar
  8. 8.
    Y. Meir, R. Blumenfeld, A. Aharony, and A. B. Harris, Phys. Rev. B 34, 3424 (1986).ADSCrossRefGoogle Scholar
  9. 9.
    Y. Meir, J. Phys. A Lett. (in press).Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Yigal Meir
    • 1
  • A. Brooks Harris
    • 1
    • 2
  • Amnon Aharony
    • 1
  1. 1.Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Theoretical PhysicsOxfordUK

Personalised recommendations