Spectral statistics near the quantum percolation threshold

The statistical properties of spectra of a three-dimensional quantum bond percolation system are 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 the finite-size scaling hypothesis, the critical quantum probability for bond occupation is found to be $p_q=0.33\mathrm{}\pm 0.01$ while the critical exponent for the divergence of the localization length is estimated as $\nu =1.35\mathrm{}\pm 0.10$. This later figure is consistent with the one found within the universality class of the standard Anderson model.