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In this paper, we consider a square lattice with correlated random hopping terms under the effect of an external electric field. We analyzed the dynamics of an initially localized electronic wave packet using a Taylor formalism to solve the Schrödinger dynamic equation. Our calculations suggest that the correlated disorder promotes a fast electronic propagation for intermediate times. When we switch on a static electric field, we observe an oscillatory behavior similar to the well-known "Bloch oscillations" phenomenology. We calculate the frequency of these oscillations, and our results are in good agreement with those predicted by the semi-classical approach used in crystalline lattices. Based on the local disorder and in the absence of extended states in our model, we discussed the stability of these apparent "Bloch oscillations". [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influence of electron-lattice interaction on the stability of uniform electronic wavepackets on chains as well as on several types of fullerenes. We will use an effective nonlinear Schrödinger equation to mimic the electron-phonon coupling in these topologies. By numerically solving the nonlinear dynamic equation for an initially uniform electronic wavepacket, we show that the critical nonlinear coupling above which it becomes unstable continuously decreases with the chain size. On the other hand, the critical nonlinear strength saturates on a finite value in large fullerene buckyballs. We also provide analytical arguments to support these findings based on a modulational instability analysis. [ABSTRACT FROM AUTHOR]

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet. [ABSTRACT FROM AUTHOR]

We study the effects of spatially long-range correlated phase disorder on the Hadamard quantum walk on a line. The shift operator is built to exhibit an intrinsic disorder distribution featuring long-range correlations. To impose such, we resort to fractional Brownian motion with power-law spectrum 1/k2α with α≥0 being the exponent that controls the degree of correlations. We discuss the scaling behavior of the walker's wave packet and report a localization-delocalization transition controlled by α. We unveil two intermediate dynamical regimes between exponential localization and full delocalization. [ABSTRACT FROM AUTHOR]