Short-time particle motion in one and two-dimensional lattices with site disorder

Abstract

As in the case of a free particle, the initial growth of a broad (relative to lattice spacing) wavepacket placed on an ordered lattice is slow (its time derivative has zero initial slope), and the spread (root mean square displacement) becomes linear in t at a long time. On a disordered lattice, the growth is inhibited for a long time (Anderson localization). We consider site disorder with nearest-neighbor hopping on one- and two-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 scales that may be relevant to the exciton motion in disordered systems.