Time evolution of models described by a one-dimensional discrete nonlinear Schrödinger equation

Abstract

The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in an adiabatic approximation. First, various sizes of nonlinear clusters embedded in an infinite linear chain are considered. 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 kinds of transition: (i) a cluster-trapping transition and (ii) a self-trapping transition. The dynamics of the quasiparticle with the end site initial excitation are found to exhibit (i) a sharp self-trapping transition, (ii) an amplitude transition in the site probabilities, and (iii) propagating solitonlike waves in large clusters. Ballistic propagation is observed in random nonlinear systems. The effect of nonlinear impurities on the superdiffusive behavior of the random-dimer model is also studied. \textcopyright{} 1996 The American Physical Society.