Fluctuations in random $RL-C$ networks: non-linear $\sigma-$ model description

TL;DR

This paper demonstrates that disordered RL-C networks, used to model electric field fluctuations in random composites, can be analyzed using Efetov's non-linear sigma model, connecting to Anderson localization theory.

Contribution

It introduces a novel approach to study disordered RL-C networks through the non-linear sigma model, bridging the gap with Anderson localization theory.

Findings

Statistical properties of RL-C networks can be described by the non-linear sigma model.

Provides a theoretical link between electric field fluctuations and Anderson localization.

Offers a new framework for analyzing disordered composite materials.

Abstract

Disordered $RL-C$ networks are known to be an adequate model for describing fluctuations of electric fields in a random metal-dielectric composite. We show that under appropriate conditions the statistical properties of such a system can be studied in the framework of the Efetov's non-linear $\sigma-$ model. This fact provides a direct link to the theory of Anderson localization.