  We prove that for a one-dimensional infinite lattice, with long-range
coupling among sites, the diffusion of an initial delta-like pulse in the bulk,
is ballistic at all times. We obtain a closed-form expression for the mean
square displacement (MSD) as a function of time, and show some cases including
finite range coupling, exponentially decreasing coupling and power-law
decreasing coupling. For the case of an initial excitation at the edge of the
lattice, we find an approximate expression for the MSD that predicts ballistic
behavior at long times, in agreement with numerical results.
