Advertisement

Flicker (1/f) Noise in Percolation Networks

  • R. Rammal
Part of the Springer Proceedings in Physics book series (SPPHY, volume 5)

Abstract

Statistical self-similarity is emerging as an important concept underlying the behavior of disordered systems. In percolation clusters, for example, the fractal dimension has been identified first /1/. Much later, the notion of spectral dimension /2/ was introduced in order to describe the spectrum of the Laplacian operator, which appears in a large variety of linear physical problems. Another intrinsic property is the recently introduced spreading dimension /3/. Intuitively, it is plausible that an infinite number of exponents must be used to characterize a fractal. In the following, we show that at least one physically measurable quantity, the magnitude (not the frequency dependence) of the resistance noise spectrum (1/f noise) depends on a new exponent pertaining to fractal lattices. We show that this exponent, b, can be seen as a member of an infinite family of exponents, which includes the fractal and spectral dimensions. Physically, the exponent b comes from a well-known fact in the 1/f noise problem: the macroscopic mean square resistance fluctuations are much more sensitive to local inhomogeneities than the square of the macroscopic resistance itself.

Keywords

Percolation Cluster Sierpinski Gasket Bond Percolation Relative Noise Percolation Network 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Kirkpatrick: in “Ill Condensed Matter, Les Houches Summer School”, Ed. R. Balian, R. Maynard and G. Toulouse (North-Holland), Amsterdam, 1979, p. 321.Google Scholar
  2. 2.
    S. Alexander, R. Orbach: J. Physique Lett. (Paris), 43, L625 (1982)CrossRefGoogle Scholar
  3. 2a.
    R. Rammal, G. Toulouse: ibid, 44, L13 (1983).CrossRefGoogle Scholar
  4. 3.
    R. Rammal, J.C. Angles d’Auriac and A. Benoit: J. Phys. A17, L491 (1984). J. C. Angles d’Auriac, A. Benoit, A.B. Harris, R. Rammal: to be published.ADSGoogle Scholar
  5. 4.
    R. Rammal, C. Tannous, A.M.S. Tremblay: Phys. Rev. A31, XXX (1985).MathSciNetGoogle Scholar
  6. 5.
    A.M.S. Tremblay, M. Nelkin: Phys. Rev. B24, 2551 (1981), and references therein.ADSGoogle Scholar
  7. 6.
    See for instance P.J. Restle, R.J. Hamilton, M.B. Weissman, M.S. Love: Phys. Rev. B31, 2254 (1985).ADSGoogle Scholar
  8. 7.
    R.D. Black, M.B. Weissman, F.M. Fliegel: Phys. Rev. B24, 7454 (1981).ADSGoogle Scholar
  9. 7a.
    J.H. Scofield, D.H. Darling, W.W. Webb: Phys. Rev. B24, 7450 (1981).ADSGoogle Scholar
  10. 8.
    R. Rammal: J. Physique Lett. 45, 1007 (1984), and references therein.CrossRefGoogle Scholar
  11. 9.
    R. Rammal: J. Physique Lett. 46, 129 (1985).CrossRefMathSciNetGoogle Scholar
  12. 10.
    R. Rammal, M.A. Lemieux, A.M.S. Tremblay: Phys. Rev. Lett. 54, 1087 (1985).CrossRefADSGoogle Scholar
  13. 10a.
    A.B. Harris, S. Kim, T.C. Lubensky: Phys. Rev. Lett. 53, 743 (1984).CrossRefADSGoogle Scholar
  14. 11.
    R. Rammal, G. Toulouse, J. Vannimenus: J. Physique (Paris), 45, 389 (1984).CrossRefMathSciNetGoogle Scholar
  15. 12.
    L. de Arcangelis, S. Redner, A. Coniglio: Phys. Rev. B (in press). We thank S. Redner for letting us know of this work prior to publication.Google Scholar
  16. 13.
    R. Rammal, C. Tannous, P. Breton, A.M.S. Tremblay: Phys. Rev. Lett. 54, XXX (1985).Google Scholar
  17. 14.
    A. Coniglio: Phys. Rev. Lett. 46, 250 (1981).CrossRefADSGoogle Scholar
  18. 15.
    A.M.S. Tremblay: Private communication.Google Scholar
  19. 16.
    J.M. Luck: Subm. to J. Phys. A (1985).Google Scholar
  20. 17.
    D.A. Rudman, J.C. Garland: Bull. Am. Phys. Soc. 29, 352 (1984).Google Scholar
  21. 18.
    J.V. Mantese et al.: Sol. State Commun. 37, 353 (1981).CrossRefADSGoogle Scholar
  22. 19.
    J.P. Straley, S.W. Kenkel: Phys. Rev. B 29, 6299 (1984).CrossRefADSGoogle Scholar
  23. 20.
    R. Rammal: to be published (1985).Google Scholar
  24. 21.
    P.M. Kogut, J.P. Straley: J. Phys. C 12, 2151 (1979).CrossRefADSGoogle Scholar
  25. 21a.
    A. Ben-Mizrahi, D. Bergman: Ibid, 14, 909 (1981).Google Scholar
  26. 22.
    B.I. Halperin, S. Feng, P.N. Sen: Subm. to Phys. Rev. Lett.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • R. Rammal
    • 1
  1. 1.Centre de Recherches sur les Très Basses TempératuresCNRSGrenoble CédexFrance

Personalised recommendations