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

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 $σ-$ model. This fact provides a direct link to the theory of Anderson localization.