  Like a free particle, the initial growth of a broad (relative to lattice
spacing) wavepacket placed on an ordered lattice is slow (zero initial slope)
and becomes linear in $t$ at long time. On a disordered lattice, the growth is
inhibited at long time (Anderson localization). We consider site disorder with
nearest-neighbor hopping on 1- and 2-dimensional systems, and show via
numerical simulations supported by the analytical study that the short time
growth of the particle distribution is faster on the disordered lattice than on
the ordered one. Such faster spread takes place on time and length scale that
may be relevant to the exciton motion in disordered systems.
