Spectral Properties of Random Reactance Networks and Random Matrix Pencils

Abstract

Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues ${\lambda }_n$ of matrix pencils $\mathbf{H}-\lambda \mathbf{W}$, with $\mathbf{W}$ being positive definite matrix and $\mathbf{H}$ a random real symmetric one. We first consider spectra of matrix pencils with independent, identically distributed entries of $\mathbf{H}$. Then we concentrate on an infinite-range ("full-connectivity") version of random $LC$ network. In all cases we calculate the mean eigenvalue density and the two-point correlation function in the framework of Efetov's supersymmetry approach. Fluctuations in spectra turn out to be the same as those provided by Wigner-Dyson theory of usual random matrices.

22 pages, RevTex, one figure added, misprints corrected

References in corpus (4)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Level Spacing of Random Matrices in an External Source
• Dielectric resonances of binary random networks
• Universal correlators for multi-arc complex matrix models

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