Dielectric resonances of binary random networks

TL;DR

This paper studies the AC conductivity and dielectric resonances of binary random impedance networks, introducing an algorithm to analyze their spectral properties and revealing multifractal local electric field distributions.

Contribution

It presents a new algorithm to determine conductance from poles and residues, enabling detailed spectral analysis of binary networks' dielectric response.

Findings

Density of resonances characterized

Distribution of spacings analyzed

Local electric fields are multifractal

Abstract

We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in terms of its poles and of the associated residues. A numerical implementation of the algorithm, on the example of the square lattice, allows a detailed investigation of the resonant dielectric response of the binary model, including the density of resonances, the spectral function, the distribution of spacings between resonances. The distribution of local electric fields at resonance is found to be multifractal.