Abstract
We show that the analogue of the transition from Gaussian to dispersive transport in hopping systems is a damping transition of the phonons in a disordered network of coupled harmonic oscillators, that is a transition from nearly free to highly damped propagation. This is demonstrated by a generalized version of the effective-medium approximation (EMA). Our EMA version includes the correct non-analytical frequency dependence of the dynamical diffusivity D(p). This corresponds to Rayleigh scattering of the long-wavelength vibrational excitations.