Abstract
Diffusion noise and Nyquist noise on fractal lattices and percolation clusters are discussed in the high- and low-frequency limits. Diffusion noise can also be considered as a sort of ‘‘1/f noise.’’ Even for system sizes much larger than the correlation length, the fractal structure of the percolation clusters reveals itself at sufficiently high frequencies through the anomalous frequency dependence , where theta is the anomalous diffusion exponent. This law takes the 1/f form in the large-theta limit and reduces to the universal Lax-Mengert law in the case of ordinary diffusion (theta=0). The new inequality -<2 for the localization β function of certain fractals is also derived. The corresponding inequality for percolation clusters is t/ν<d where t is the conductivity exponent and ν the correlation length exponent.
- Received 10 April 1986
DOI:https://doi.org/10.1103/PhysRevB.34.7802
©1986 American Physical Society