Flicker (1/f) Noise in Percolation Networks
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.
KeywordsCovariance Percolate Iterate Cell
Unable to display preview. Download preview PDF.
- 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
- 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
- 13.R. Rammal, C. Tannous, P. Breton, A.M.S. Tremblay: Phys. Rev. Lett. 54, XXX (1985).Google Scholar
- 15.A.M.S. Tremblay: Private communication.Google Scholar
- 16.J.M. Luck: Subm. to J. Phys. A (1985).Google Scholar
- 17.D.A. Rudman, J.C. Garland: Bull. Am. Phys. Soc. 29, 352 (1984).Google Scholar
- 20.R. Rammal: to be published (1985).Google Scholar
- 21a.A. Ben-Mizrahi, D. Bergman: Ibid, 14, 909 (1981).Google Scholar
- 22.B.I. Halperin, S. Feng, P.N. Sen: Subm. to Phys. Rev. Lett.Google Scholar