Flicker (1/f) Noise in Percolation Networks

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.