Long-ranged model of random RL-C network

Disordered RL-C networks are known to be an adequate model for describing fluctuations of electric fields in a random metal–dielectric composite. These fluctuations reflect the presence of “dielectric resonances” which are poles of the conductance of dissipationless LC networks. In this paper I give an account of recent work on statistical properties of a long-ranged version of RL-C network (Y.V. Fyodorov, J. Phys. A 32 (1999) 7429; Y.V. Fyodorov JETP Lett. 70 (1999)). The main goal is to show that it can be studied analytically in the framework of the Efetovʹs nonlinear σ-model. As a particular example, I study the two-point spectral correlation function of the electric potentials at a given lattice node. For infinite-ranged (“full connectivity”) networks fluctuations turn out to be the same as those provided by the Wigner–Dyson theory of usual random matrices. For networks with a finite range of connectivity Anderson localization effects modify the statistics.