Trapping Effects in Surface Diffusion

  • Lazaros K. Gallos
  • Panos Argyrakis
Part of the NATO ASI Series book series (NSSB, volume 360)


We consider the classical problem of particles diffusing on a lattice that contains a random distribution of static traps of low concentration. We use the known Donsker-Varadhan analytical solutions, which we modify for 2-D lattices, to get good agreement with very elaborate numerical results for the survival probability at finite times. This is done through the distribution of the number of distinct sites visited in the absence of traps. Our final formula is also of exponential form, in which the constants are derived from the numerical simulation data.


Random Walk Survival Probability Finite Time Exponential Form Static Trap 
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  1. 1.
    M.D. Donsker and S.R.S. Varadhan, “Asymptotics for the Wiener sausage”, Commun. Pure Appl. Math. 28, 525 (1975).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    F. den Hollander and G.H. Weiss, “Aspects of trapping in transport processes”, in: Contemporary Problems in Statistical Physics G.H. Weiss, ed., SIAM, Philadelphia (1994).Google Scholar
  3. 3.
    J.K. Anlauf, “Asymptotically exact solution of the one-dimensional trapping problem”, Phys. Rev. Lett. 52, 1845 (1984).ADSCrossRefGoogle Scholar
  4. 4.
    P. Grassberger and I. Procaccia, “The long time properties of diffusion in a medium with static traps”, J. Chem. Phys. 77, 6281 (1982).ADSCrossRefGoogle Scholar
  5. 5.
    H.B. Rosenstock, “Random walks on lattices with traps”, J. Math. Phys., 11, 487 (1970).ADSCrossRefGoogle Scholar
  6. 6.
    G. Zumofen and A. Blumen, “Random walk studies of excitation trapping in crystals”, Chem. Phys. Lett. 88, 63 (1982).ADSCrossRefGoogle Scholar
  7. 7.
    R.F. Kayser and J.B. Hubbard, “Diffusion in a medium with a random distribution of static traps”, Phys. Rev. Lett. 51, 79 (1983).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    D.C. Torney, “Variance of the range of a random walk”, J. Stat. Phys. 44, 49 (1986).ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    T.C. Lubensky, “Fluctuations in random walks with random traps”, Phys. Rev. A 30, 2657 (1984).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    S. Havlin, M. Dishon, J.E. Kiefer, and G.H. Weiss, “Trapping of random walks in two and three dimensions”, Phys. Rev. Lett. 53, 407 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    J.K. Anlauf, PhD dissertation (1988).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Lazaros K. Gallos
    • 1
  • Panos Argyrakis
    • 1
  1. 1.Department of PhysicsUniversity of ThessalonikiThessalonikiGreece

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