  We investigate diffusion of excitation in one- and two-dimensional lattices
with random on-site energies and deterministic long-range couplings (hopping)
inversely proportional to the distance. Three regimes of diffusion are observed
in strongly disordered systems: ballistic motion at short time, standard
diffusion for intermediate times, and a stationary phase (saturation) at long
times. We propose an analytical solution valid in the strong-coupling regime
which explains the observed dynamics and relates the ballistic velocity,
diffusion coefficient, and asymptotic diffusion range to the system size and
disorder strength via simple formulas. We show also that in the long-time
asymptotic limit of diffusion from a single site the occupations form a
heavy-tailed power-law distribution.
