Spectral statistics near the quantum percolation threshold

Abstract

The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in which the density of states is rather smooth are analyzed. Using finite size scaling hypothesis, the critical quantum probability for bond occupation is found to be $p_q=0.33\pm.01$ while the critical exponent for the divergence of the localization length is estimated as $ν=1.35\pm.10$. This later figure is consistent with the one found within the universality class of the standard Anderson model.