Dois elétrons interagentes em cadeias aperiódicas

Abstract

Recently, the dynamic location and its relationship with interacting electrons hás attracted great interest on Physics, being subject of several studies. In this Master's Degree dissertation we present targeted studies to two interacting electrons in a one-dimensional lattice, whose potentials distribution is aperiodic. This type of distribution is characterized by a behavior that changes between the periodic and random case. Employing numerical and computational methods, we solve the Schrödinger equation to study the stationary eigenstates and the system dynamics, verifying the influence of the interactions between electrons. In the analysis of eigenstates we observed that the presence of interaction promotes a weakening of electron localization induced by disorder, agreeing with the existing literature. The dynamics aspects of the electrons show that the existence of a local field, natural of this potential distribution, promotes an oscillation of the wavepacket in extended phase. The contribution of the local field becomes more evident when the two electrons are subject to an external electric field, since the frequency of Bloch's oscillations is altered in function of initial conditions of the system. The analysis of the numerical results will be treated trough of a semi-classical formalism, characterizing the frequencies of Bloch's oscillations to systems with two electrons in aperiodic chains.