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 


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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

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