Localization behavior of vibrational modes

After a short introduction into percolation theory we discuss the localizat ion behavior of vibrational modes of infinite percolation clusters above th e critical concentration in two and three dimensions. Results from level st atistics show that all eigenstates are localized in d = 2, including the lo w frequency phonon states. In d = 3 there is evidence for a localization-de localization transition. But contrary to the common view this transition oc curs for frequencies above the phonon-fracton crossover giving rise to a ne w regime of extended fracton states.