Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent

The excess 1/f noise in a random lattice with bond resistances r similar to exp(-lambda x), where x is a random variable and lambda much greater than 1, is studied theoretically. It is shown that if the correlation function {delta r(2)}similar to r(theta+2), then the relative spectral density of the noise in the system is expressed as C-e similar to lambda(m) exp(-lambda(1-p(c)), where p(c) is the percolation threshold and m = vd (v is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the theta-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m = 2.3 for theta = 1 and theta = 0, in agreement with the hypothesis. (C) 1996 American Institute of Physics.