Wave functions in the Anderson model and in the quantum percolation model:a comparison

We compare numerically the localization behavior of electronic eigenfunctio ns in the Anderson model and on self-similar percolation clusters at critic ality. We find that the distributions of the local wave function amplitudes \psi\ at fixed distances from the localization center are very similar for both models; The amplitude distributions are well approximated by log-norm al fits, which seem to become exact at large distances. From the distributi ons, we can calculate analytically the behavior of the averages at sufficie ntly large distances. We observe two different localization regimes. In the first regime, at intermediate distances from the localization center, we f ind stretched exponential localization ('sublocalization'), ln[\psi\] simil ar to -r(d psi), with effective localization exponents d(psi) < 1. In the s econd regime, for very large r, the averages strongly depend on the number of configurations N, and superlocalization (d(psi) > 1) is observed, conver ging to simple exponential behavior asymptotically as expected. The crossov er from the intermediate to the asymptotic regime depends logarithmically o n the number of configurations.