Transporte em baixa dimensionalidade na presença de não-linearidade e desordem

Abstract

In this PhD thesis we consider the effect of nonlinearity and correlated disorder in lowdimensional electronic systems. We study the dynamics of one electron wave packet in a chain with a nonadiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schr¨odinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the bandwidth. We show that a weaker nonlinearity is required to produce self-trapping in the regime of short delay times. However, this trend is reversed for slow nonlinear responses, resulting in a reentrant phase diagram. In slowly responding media, self-trapping only takes place for very strong nonlinearities. In additional we consider the two-dimensional Anderson model with correlated disorder. We bring our attention to an Anderson model with diagonal disorder diluted by an underlying periodicity. The model consists of two interpenetrating sublattices, one composed of random potentials (Anderson lattice) and the other composed of non-random constant potentials. By using numerical calculations we compute the localization properties and provide a accurate estimates of the level spacing distribution. Within our numerical precision we demonstrate that the states close to band center obey a Wigner-Like distribution. For strong disorder a intermediate Poisson-Wigner-Like level spacing distribution is obtained.