Fluctuations and scaling of inverse participation ratios in random binary resonant composites

Abstract

We study the statistics of local-field distribution solved by the Green's-function formalism [Y. Gu et al., Phys. Rev. B 59, 12847 (1999)] in disordered binary resonant composites. For a percolating network, inverse participation ratios (IPR's) with $q=2$ are illustrated, as well as typical local-field distributions of localized and extended states. Numerical calculations indicate that for a definite fraction p the distribution function of the IPR ${P}_{q}$ has a scale invariant form. We also show the scaling behavior of the ensemble-averaged $〈{P}_{q}〉$ described by the fractal dimension ${D}_{q}.$ To relate the eigenvector correlations to resonance level statistics, the axial symmetry between ${D}_{2}$ and the spectral compressibility $\ensuremath{\chi}$ is obtained.