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In this paper we study a one-dimensional ternary harmonic chain with the mass distribution constructed from an Ornstein-Uhlenbeck process. We generate a ternary mass disordered distribution by generating the correlated Ornstein-Uhlenbeck process and mapping it into a sequence of three different values. The probability of each value is controlled by a fixed parameter b. We analyze the localization aspect of the above model by numerical solution of the Hamilton equations and by the transfer matrix formalism. Our results indicate that the correlated ternary mass distribution does not promote the appearance of new extended modes. In good agreement with previous work, we obtain extended modes for b → ∞; however, we explain in detail the main issue behind this apparent localization- delocalization transition. In addition, we obtain the energy dynamics for this classical chain.

In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron-soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling.

In this paper, we study the dynamics of a one-electron in a one-dimensional (1d) alloy with a correlated Ornstein-Uhlenbeck (OU) disorder distribution. The model considered here corresponds to an alloy with three types of atoms where the position of each atom is obtained using a stochastic rule based on the OU process. We analyze in detail the e®ect of this correlated disorder in the optical absorption spectrum and the level spacing statistics near the band center. Our results reveal a new collection of optical absorption peaks. We explain in details the appearance of each peak. Our calculations about the level spacing's distribution reveals a Poisson distribution thus contradicting previous statements about the existence of extended states in ternary electronic models with correlated disorder distribution.

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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.

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