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We study one-dimensional harmonic chains in which clusters of two or three defect atoms are embedded randomly. The disorder in the systems appean in the masses of the atoms. Reflectionless modes are obtained by studying different kinds of correlation among the m e s . The localization behaviour of the modes around these special frequencies is examined analytically a s well as numerically. To discem the nature of the modes at and around those frequencies, density of states, bandwidth scaling and site Green functions are sNdied. If the special frequencies lie within the common band of the constituent atoms and at zero the modes are extended ak and around them. However, the modes are critical when the special frequency appears at the upper band edge of the host system. The number of non-scatted modes is estimated for all cases. It isf i for the dimer problem. For the trimer problem with degenerate resonances appearing inside the constituent band it is -N3/'. If Ule degenerate resonances of the trimer appear at W O freqency the number of non-scattered modes is -NSl6.

The dynamics of models described by a one-dimensional discrete nonlinear Schrödinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. First, various sizes of nonlinear cluster 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 selftrapping 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 soliton-like waves in large clusters. Ballistic propagation is observed in random nonlinear systems. The effect of nonlinear impurities on the superdiffusive behavior of random-dimer model is also studied.

Dynamics of a particle in a perfect chain with one nonlinear impurity and in a perfect nonlinear chain under the action of dc field is studied numerically. The nonlinearity appears due to the coupling of the electronic motion to optical oscillators that are treated in the adiabatic approximation. We study both the cases of low and high values of field strength. Three different ranges of nonlinearity are obtained each of which has a different dynamics. In the low and intermediate ranges of nonlinearity, the localization effects are reduced. In fact, in the intermediate range case subdiffusive behavior in the perfect nonlinear chain is obtained for a long time. In all cases a critical value of nonlinear strength exists where a self-trapping transition takes place. This critical value depends on the system and the field strength. Beyond the self-trapping transition, nonlinearity enhances the localization. ͓S0163-1829͑98͒05434-4͔

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