Conductance fluctuations in random resistor networks with hyperuniform disorder

TL;DR

This paper investigates conductance fluctuations in hyperuniform disordered resistor networks, revealing that such fluctuations scale as $L^{-d/2}$ and are not suppressed despite hyperuniformity.

Contribution

The study demonstrates that conductance fluctuations in hyperuniform disordered networks do not diminish as expected, providing new insights into their scaling behavior.

Findings

Conductance fluctuations scale as $L^{-d/2}$ in hyperuniform networks.

Hyperuniform disorder does not suppress conductance fluctuations as previously expected.

Numerical results are provided for two-dimensional networks.

Abstract

We study conductance fluctuations in random resistor networks with hyperuniform bond disorder, where the fluctuations of the number of bonds present in a test volume $V$ scale as $V^{-a}$ with $a > 1/2$. Since small changes in the concentration of bonds present in a local region give rise to a proportionate increase in the locally averaged conductance, one may expect that in hyperuniform disorder, conductance fluctuations will also show suppressed fluctuations. We argue that this is not the case: conductance fluctuations scale as $L^{-d/2}$ for a sampling size $L$. We show numerical results for $d=2$.