Statistics of level spacing of geometric resonances in random binary composites

Abstract

We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing distribution $P(t)$ and level number variance $\hat{I}{\pounds }^2(L)$ have the general features. It is also shown that the short-range fluctuation $P(t)$ and long-range spectral correlation $\hat{I}{\pounds }^2(L)$ lie between the profiles of the Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation threshold $p_c$, crossover behavior of functions $P(t)$ and is obtained, giving the finite size scaling of mean level spacing $\hat{I}´$ and mean level number $n$, which obey the scaling laws, and $n=0.911L^{1.970}$.

11 pages, 7 figures,submitted to Phys. Rev. B