Finite Coherence Length of Thermal Noise in Percolating Systems

Abstract

Noise has been measured in two types of coductor-insulator mixtures as a function of bias and composition. It was marked by a huge increase in magnitude as the resistance increased only slightly due to Joule heating. The noise (resistance) current scale $I_s$($I_r$) for nonlinearity were found to scale with the linear resistance $R_o$ as $I_s(I_r) \sim {{R_o}^ {-x_s(x_r)}}$ where the exponent $x_s$ is equal to 0.80 and 0.68 in carbon-wax and carbon-polyethylene respectively and $x_r \approx 0.5$. It is shown that the large increase of noise in nonohmic regime as well as the differences between the noise and resistance exponents are due to the finite-sized inequilibrium thermal fluctuations whose coherence length is same as the correlation length of the underlying percolating systems. A expression for $x_s$ is derived.