"Creeping conductance" in nonstationary granular systems and artificial arrays

TL;DR

This paper models nonstationary granular systems with fluctuating resistances, analyzing charge transfer during electrical breakdowns to understand conductivity, relaxation, and fluctuations, with potential applications in colloidal and polymer-linked grain arrays.

Contribution

It introduces a classical approximation model for nonstationary conductor arrays with time-fluctuating resistances, focusing on charge transfer during breakdowns.

Findings

Derived expressions for conductivity and relaxation rates.

Analyzed fluctuations in charge transfer.

Applicable to colloidal and polymer-linked systems.

Abstract

We consider a nonstationary array of conductors, connected by resistances that fluctuate with time. The charge transfer between a particular pair of conductors is supposed to be dominated by "electrical breakdowns" -- the moments when the corresponding resistance is close to zero. An amount of charge, transferred during a particular breakdown, is controlled by the condition of minimum for the electrostatic energy of the system. We find the conductivity, relaxation rate, and fluctuations for such a system within the "classical approximation", valid, if the typical transferred charge is large compared to $e$. We discuss possible realizations of the model for colloidal systems and arrays of polymer-linked grains.