Direct Observation of Localized Fractons Excited on Percolating Nets

Abstract

We have performed supercomputer simulations in order to gain insight into the nature of localized fractons excited on percolation nets. It is found that fracton modes possess a quite unique character, i.e., the core of fracton excitations falls off sharply at their edges. This is in contrast with the case of homogeneously extended modes (phonons), in which the change in their amplitudes is correlated smoothly over a long distance. In this connection, ensemble averaging over as many as one hundred fractons yields evidence of the strong localization of these modes which are quite different from the usual localized excitations.