Localização em sistemas com desordem correlacionada : correlações exponenciais e correlações tipo Ornstein-Uhlenbeck

Abstract

In this work, we numerically calculate the dynamics of an electron in one-dimensional disordered systems. Our formalism is based on the numerical solution of the time-dependent Schrodinger equation for the complete Hamiltonian combined with a finite-size scaling analysis. Our calculations were perfomed on chains with short-ranged exponential correlation on the diagonal disorder distribution. Our formalism provides an accurate estimate for the dependence of the localization length with the width of disorder. We also show here numerical calculations of the localization length by using a standard renormalization procedure. Our results agree within our numerical precision. We provide a detailed description of the role played by these short-range correlations within electronic transport. We numerically demonstrate the relationship between localization length, correlation length, and the strenght of disorder. Following the study, we analyzed a a one-dimensional ternary harmonic chain with the mass distribution constructed from a 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 the 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 agreements with previous works, we obtain extended modes for b (finite)) 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.