TIME EVOLUTION OF MODELS DESCRIBED BY A ONE-DIMENSIONAL DISCRETE NONLINEAR SCHRODINGER-EQUATION

The dynamics of models described by a one-dimensional discrete nonline ar Schrodinger equation is studied. The nonlinearity in these models a ppears due to the coupling of the electronic motion to optical oscilla tors which are treated in an adiabatic approximation. First, various s izes of nonlinear clusters embedded in an infinite linear chain are co nsidered. The initial excitation is applied either at the end site or at the middle site of the cluster. In both the cases we obtain two kin ds of transition: (i) a cluster-trapping transition and (ii) a self-tr apping transition. The dynamics of the quasiparticle with the end site initial excitation are found to exhibit (i) a sharp self-trapping tra nsition, (ii) an amplitude transition in the site probabilities, and ( iii) propagating solitonlike waves in large clusters. Ballistic propag ation is observed in random nonlinear systems. The effect of nonlinear impurities on the superdiffusive behavior of the random-dimer model i s also studied.