Scattering of fractons, the Ioffe-Regel criterion, and the (4/3) conjecture

The relaxation time for scattering of vibrational modes by structural irregularities in d-dimensional random systems is shown to cross over from 1/d+1c-d for phonons (<c, the crossover frequency between phonon and fracton vibrational excitations) to 5-3d for fractons (d is the fracton dimensionality). The Ioffe-Regel criterion for localization, 1, and a scaling Ansatz, then lead to the Alexander-Orbach value, di=(4/3), and 1/ for all >c.. AE