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In this work, we study a tight-binding Hamiltonian model system of a binary correlated ladder with diluted disorder. We introduce intra-chain correlations between the on-site potentials by imposing that ϵ(i, s) = - ϵ(i, - s) where s = ± 1 indexes the two ladder chains. Further, we consider each ladder chain as composed of inter-penetrating ordered and random sub-chains. We show that the presence of a random on-site distribution in one of the inter-penetrating chains leads to Anderson localization except at a specific symmetric pair of energy eigenmodes. Further, by integrating the time-dependent Schroedinger equation, we follow the time-evolution of an initially localized one-electron wavepacket. We report that the remaining delocalized resonant modes are responsible for a super-diffusive spread of the wavepacket dispersion while the wavepacket participation function remains finite. A scaling analysis of the wavepacket distribution shows that it obeys a universal scaling form with the development of a power-law tail followed by a super-diffusively evolving cutoff. We obtain three exponents characterizing this super-diffusive dynamics and show that they satisfy a simple scaling relation.

In this paper, we investigate the one-electron propagation in a nonlinear chain with electron–lattice interaction. The model contains standard cubic nonlinear terms, and we introduce the coupling between the electron and the lattice through the hopping distribution. We solve the coupled equation set to electron and lattice and calculate the electronic position as a function of time. We provide a detailed investigation of the electron and lattice dynamics for a wide range of electron–lattice coupling intensities. Our results demonstrate that depending on the initial condition we consider and the intensity of the electron–lattice interaction, we can obtain (or not) an electron–phonon pair formation. Our results reveal that, depending on the initial velocity of the lattice and the degree of electron–lattice term, we can observe a repulsion between electron and lattice deformations. [ABSTRACT FROM AUTHOR]

We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated by using a sinusoidal function whose phase varies as a power-law, $\phi \propto n^{\nu}$, where n labels the positions along the media. By considering a discrete one-dimensional version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity. [ABSTRACT FROM AUTHOR]

We consider interacting electrons moving in a nonlinear Morse lattice. We set the initial conditions as follows: electrons were initially localized at the center of the chain and a solitonic deformation was produced by an impulse excitation on the center of the chain. By solving quantum and classical equations for this system numerically, we found that a fraction of electronic wave function was trapped by the solitonic excitation, and trapping specificities depend on the degree of interaction among electrons. Also, there is evidence that the effective electron velocity depends on Coulomb interaction and electron-phonon coupling in a nontrivial way. This association is explained in detail along this work. In addition, we briefly discuss the dependence of our results with the type of initial condition we choose for the electrons and lattice. [ABSTRACT FROM AUTHOR]