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

TL;DR

This paper investigates the statistical properties and scaling behavior of inverse participation ratios in disordered binary resonant composites, revealing scale invariance and fractal characteristics of local field distributions.

Contribution

It introduces a detailed analysis of IPR distributions and their scaling in binary resonant composites, linking eigenvector correlations to resonance level statistics.

Findings

IPR distribution functions exhibit scale invariance.

Ensemble-averaged IPR scales with fractal dimension D_q.

Identifies symmetry between D_2 and spectral compressibility .

Abstract

We study the statistics of local field distribution solved by the Green's-function formalism (GFF) [Y. Gu et al., Phys. Rev. B {\bf 59} 12847 (1999)] in the disordered binary resonant composites. For a percolating network, the inverse participation ratios (IPR) with $q=2$ are illustrated, as well as the typical local field distributions of localized and extended states. Numerical calculations indicate that for a definite fraction $p $ the distribution function of IPR $P_q$ has a scale invariant form. It is also shown the scaling behavior of the ensemble averaged $<P_{q}>$ described by the fractal dimension $D_q$. To relate the eigenvectors correlations to resonance level statistics, the axial symmetry between $D_2$ and the spectral compressibility $\chi$ is obtained.