Dynamical delocalization in one-dimensional disordered systems with oscillatory perturbation.

Abstract

The effect of dynamical perturbation on the quantum localization phenomenon in a one-dimensional disordered quantum system (1DDS) is investigated systematically by a numerical method. The dynamical perturbation is modeled by an oscillatory driving force containing M independent (mutually incommensurate) frequency components. For M>or=2 a diffusive behavior emerges and in the presence of the finite localization length of the asymptotic wave packet can no longer be detected numerically. The diffusive motion obeys a subdiffusion law characterized by the exponent alpha as xi(t)(2) proportional t(alpha), where xi(t)(2) is the mean square displacement of the wave packet at time t. With an increase in M and/or the perturbation strength, the exponent alpha rapidly approaches 1, which corresponds to normal diffusion. Moreover, the space-time (x-t) dependence of the distribution function P(x,t) is reduced to a scaled form decided by alpha and another exponent beta such that P(x,t) approximately exp(-constx(x/t(alpha/2))(beta)), which contains the two extreme limits, i.e., the localization limit (alpha=0, beta=1) and the normal-diffusion limit (alpha=1, beta=2) in a unified manner. Some 1DDSs driven by the oscillatory perturbation in different ways are examined and compared.