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Anomalous diffusion in disordered lattices: Effect of bias

  • E. Arapaki
  • P. Argyrakis
  • I. Avramov
  • A. Milchev
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 519)

Abstract

We model a system of disorder by utilizing a lattice on which the sites are characterized by energies, which are highly disordered, as they are chosen from a given distribution of energy values (say, from a uniform distribution in a given range), and thus every single site is characterized by a different energy value. Diffusion of single isolated particles is thermally activated, and follows Boltzmann statistics. The behavior of the mean-square displacement is followed as a function of time. It has been observed in the past that in such a system there is a strong anomaly at early times, in that the system is strongly sub-linear, but crosses over to the classical expected linear behavior at long times.

In this system we now consider an additional effect, that of directional bias in the motion. A higher probability is assigned in a prescribed direction, which naturally leads to ballistic motion. An interesting effect is observed as the temperature is raised to very high values: motion crosses over to normal diffusion with increasing temperature, even in the presence of the bias. This effect is in addition to the previously observed sub-diffusional motion at early times, which is also observed here, and also crosses over to normal diffusion at long times. The interplay between these factors of the two crossover points is of considerable interest, and it is examined here in detail. The pertinent scaling laws are given for the crossover times.

Furthermore, we consider the case of the dependence of the bias on some frequency, which makes it to alternate (switch) the direction of motion with the given frequency parameter, resulting in a rachet-type of picture, and in a different type of scaling.

Keywords

Percolation Threshold Anomalous Diffusion Normal Diffusion Bias Direction Ballistic Motion 
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.

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References

  1. Arapaki E., Argyrakis P., Avramov I., Milchev A. (1997): Phys. Rev. E 56, R29Google Scholar
  2. Argyrakis P., Kopelman R., (1981): Chem. Phys. 57, 29CrossRefGoogle Scholar
  3. Argyrakis P., Kopelman R., (1983): Chem. Phys. 78, 251CrossRefGoogle Scholar
  4. Argyrakis P., Milchev A., Pereyera V., Kehr K.W. (1995): Phys. Rev. E 52, 3623CrossRefADSGoogle Scholar
  5. Avramov I., Milchev A., (1988): J. Non-Cryst. Solids 104, 253CrossRefADSGoogle Scholar
  6. Avramov I., (1991): J. Chem. Phys. 25, 4439CrossRefADSGoogle Scholar
  7. Avramov I., Milchev A., Argyrakis P. (1993): Phys. Rev. E 47, 2303CrossRefADSGoogle Scholar
  8. Bouchaud J.P., Georges A. (1990): Phys. Rep. 125, 127CrossRefADSMathSciNetGoogle Scholar
  9. Dafano A., Jacucci G., (1977): Phys. Rev. Lett. 39, 950CrossRefADSGoogle Scholar
  10. Dafano A., Jacucci G., (1978): J. Nucl. Matter 69/70, 549CrossRefADSGoogle Scholar
  11. Dialynas T.E., Lindenberg K., Tsironis G.P., (1997): Phys. Rev. E 56, 3976CrossRefADSGoogle Scholar
  12. Druger, S.D., Nitzan, A., Ratner, M.A. (1983): J. Chem. Phys. 79, 3133CrossRefADSGoogle Scholar
  13. Druger S.D., Ratner M.A., Nitzan A., (1985): Phys. Rev. B 31, 3939ADSGoogle Scholar
  14. Dyre J.C., (1994): Phys. Rev. B 49, 11709CrossRefADSGoogle Scholar
  15. Dyre J.C., Jacobsen J.M., (1995): Phys. Rev. E 52, 2429ADSGoogle Scholar
  16. Faucheaux L.P., Bourdieu L.S., Kaplan P.D., Libchaber A.J., (1995): Phys. Rev. Lett. 74, 1504CrossRefADSGoogle Scholar
  17. Haus J., Kehr K.W. (1987): Phys. Rep. 150, 263CrossRefADSGoogle Scholar
  18. Hörner A., Milchev A., Argyrakis P. (1995): Phys. Rev. E 52, 3570CrossRefADSGoogle Scholar
  19. Lottner V., Haus J.W., Heim A., Kehr K.W., (1979): J. Phys. Chem. Solids 40, 557CrossRefADSGoogle Scholar
  20. Magnasco M.O., (1993): Phys. Rev. Lett. 71, 1477CrossRefADSGoogle Scholar
  21. Magnasco M.O., (1994): Phys. Rev. Lett. 72, 2656CrossRefADSGoogle Scholar
  22. Marchesoni F., (1997): Phys. Rev. E 56, 2492CrossRefADSGoogle Scholar
  23. Nitzan A., Ratner M.A., (1994): J. Chem. Phys. 98, 1765CrossRefGoogle Scholar
  24. Sapag K., Pereyra V., Riccardo J.L., Zgrablich G. (1993): Surf. Sci. 295, 433CrossRefADSGoogle Scholar
  25. Vattulainen, I., Merikoski, J., Ala-Nissila, T., Ying, S.C. (1996): Surf. Sci. 366, L697Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • E. Arapaki
    • 1
  • P. Argyrakis
    • 1
  • I. Avramov
    • 2
  • A. Milchev
    • 2
  1. 1.Department of PhysicsUniversity of ThessalonikiThessalonikiGreece
  2. 2.Institute for Physical ChemistryBulgarian Academy of SciencesSofiaBulgaria

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