Spectral Properties of Random Reactance Networks and Random Matrix Pencils

Details Spectral Properties of Random Reactance Networks and Random Matrix Pencils Spectral Properties of Random Reactance Networks and Random Matrix Pencils

1999-06-06

arxiv.org/abs/cond-mat/9906085v2

J.Phys.A v.32 (1999) pp.7429-7446

Physics

Condensed Matter

22 pages, RevTex, one figure added, misprints corrected

Scientific paper

10.1088/0305-4470/32/42/314

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 ${\bf H}-\lambda {\bf W}$, with ${\bf W}$ being positive definite matrix and ${\bf H}$ a random real symmetric one. We first consider spectra of matrix pencils with independent, identically distributed entries of ${\bf H}$. 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.

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