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We present a statically disordered electronic system in which under certain circumstances an initially localized particle necessarily becomes delocalized at long times regardless of the spatial dimension and the magnitude of the disorder. The model is based on correlations between diagonal and off-diagonal matrix elements and is shown to be applicable to structurally induced disorder in solids. Numerical and analytical calculations in one dimension indicate that transport is superdiffusive, with the mean-square displacement growing in time as t', regardless of the magnitude of the disorder. Transport is shown to arise in this model from a set of measure-zero unscattered states at a particular energy in the parent-ordered band. It is argued that, when the Fermi level coincides with the energy of the unscattered states, an enhancement of transport should obtain. In addition, it is shown that superdiffusive motion persists for a wide range of correlations between the diagonal and off-diagonal matrix elements when the disorder is structurally induced and chosen from a bivalued distribution. The relevance of these results to transport experiments is discussed.

Classical Ablowitz-Ladik type soliton dynamics from three closely related classical nonlinear equations is studied using a perturbative method. Model nonintegrable equations are derived by assuming nearest neighbor hopping of an exciton(vibron) in the presence of a full exciton(vibron)-phonon interaction in soft molecular chains in general and spines of alpha-helices in particular. In all cases, both trapped and moving solitons are found implying activation energy barrier for propagating solitons. Analysis further shows that staggered and nearly staggered trapped solitons will have a negative effective mass. In some models the exciton(vibron)-phonon coupling affects the hopping. For these models, when the conservation of probability is taken into account, only propagating solitons with a broad profile are found to be acceptable solutions. Of course, for the soliton to be a physically meaningful entity, total nonlinear coupling strength should exceed a critical value. On the basis of the result, a plausible modification in the mechanism for biological energy transport involving conformational change in alpha-helix is proposed. Future directions of the work are also mentioned.

The Discrete Nonlinear Schrödinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form −χ | C | σ where σ is arbitrary and χ is the nonlinearity parameter are considered. Furthermore, | C | represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity −χ | C | σ , three values of | χ cr |, namely, | χ cr |= 2, at σ = 0 and | χ cr |= 1 and 8 3 for σ = 2 are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed. PACS numbers : 71.55.-i, 72.10.Fk Typeset using REVT E X