Scaling Law of Resistance Fluctuations in Stationary Random Resistor Networks

In a random resistor network we consider the simultaneous evolution of two competing random processes consisting in breaking and recovering the elementary resistors with probabilities WD and WR. The condition WR > WD/(1+ WD) leads to a stationary state, while in the opposite case, the broken resistor fraction reaches the percolation threshold pc. We study the resistance noise of this system under stationary conditions by Monte Carlo simulations. The variance of resistance fluctuations <DR^2> is found to follow a scaling law |p - p_c|^-k_0 with k_0 = 5.5. The proposed model relates quantitatively the defectiveness of a disordered media with its electrical and excess-noise characteristics.