Diffusion noise of fractal networks and percolation clusters.

Diffusion noise and Nyquist noise on fractal lattices and percolation clusters are discussed in the highand 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 f "+@~"+e',where 8 is the anomalous diffusion exponent. This law takes the 1/f form in the large-8 limit and reduces to the universal Lax-Mengert law f ' in the case of ordinary diffusion (8=0). The new inequality —PL ~2 for the localization P function of certain fractals is also derived. The corresponding inequality for percolation clusters is t/v g d where t is the conductivity exponent and v the correlation length exponent.