Scaling Law of Resistance Fluctuations in Stationary Random Resistor Networks

Abstract

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 ${W}_{D}$ and ${W}_{R}$. The condition ${W}_{R}>{W}_{D}/({1+W}_{D})$ leads to a stationary state, while in the opposite case, the broken resistor fraction reaches the percolation threshold ${p}_{c}$. We study the resistance noise of this system under stationary conditions by Monte Carlo simulations. The variance of resistance fluctuations $〈\ensuremath{\delta}{R}^{2}〉$ is found to follow a scaling law $|{p\ensuremath{-}p}_{c}{|}^{\ensuremath{-}{\ensuremath{\kappa}}_{0}}$ with ${\ensuremath{\kappa}}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.5$. The proposed model relates quantitatively the defectiveness of a disordered media with its electrical and excess-noise characteristics.