Finite Coherence Length of Thermal Noise in Percolating Systems

TL;DR

This paper investigates the finite coherence length of thermal noise in percolating systems, revealing how nonohmic noise behavior relates to thermal fluctuations and system correlation length, with experimental and theoretical insights.

Contribution

It introduces a model linking thermal fluctuation coherence length to noise behavior in percolating systems, supported by experimental measurements and derived expressions.

Findings

Noise magnitude increases sharply with resistance due to Joule heating

Scaling laws for nonlinearity thresholds with resistance are established

Finite thermal fluctuation coherence length explains noise and resistance exponent differences

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.