A square tight-binding lattice model, where the hopping integrals t0 of surface (edge or boundary) sites are different from the hopping integrals t1 of interior (bulk) sites, is used to show the effect of edges on dynamics and (de) localization. The quantum propagation dynamics of a particle, or the time dependence of a state vector initially localized on a surface site (for example, on the first site (1, 1)), and the probability distribution averaged over time are studied. For each lattice, there exists a value of t0=t(subscript c) at which the highest degree of delocalization of the propagation occurs. We show that the propagation of a particle initially localized on a surface site undergoes a transition from being localized over the surface layer to being delocalized over the whole lattice as t0 changes. This transition is described by an exponential law (y=ae(subscript -x/b)+y0) when t0<t(subscript c), but by a power law when t0>t(subscript c).
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