Density of States Approach to Electric Field Fluctuations in Composite Media

TL;DR

This paper investigates the spatial fluctuations of local electric fields in composite media, revealing density of states features similar to van Hove singularities, which are useful for characterizing field fluctuations and are affected by disorder.

Contribution

It introduces an analytical and numerical study of electric field fluctuations in composite media, highlighting the role of density of states and critical points in the spectra.

Findings

Density of states exhibits sharp peaks at critical points.

Critical points relate to saddle and inflection points in field spectra.

Disorder broadens and diminishes these spectral singularities.

Abstract

Spatial fluctuations of the local electric field induced by a constant applied electric field in composite media are studied analytically and numerically. It is found that the density of states for the fields exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. As in solids, these singularities are generally related to saddle and inflection points in the field spectra and are of considerable value in the characterization of the field fluctuations. The critical points are very prominent in dispersions with a regular, ``crystal-like'', structure. However, they broaden and eventually disappear as the disorder increases.