Localization and delocalization properties in quasi-periodically-driven one-dimensional disordered systems

Localization and delocalization of quantum diffusion in a time-continuous one-dimensional Anderson model perturbed by the quasiperiodic harmonic oscillations of M colors is investigated systematically, which has been partly reported by a preliminary Letter [H. S. Yamada and K. S. Ikeda, Phys. Rev. E 103, L040202 (2021)]. We investigate in detail the localization-delocalization characteristics of the model with respect to three parameters: the disorder strength W, the perturbation strength epsilon, and the number of colors, M, which plays the similar role of spatial dimension. In particular, attention is focused on the presence of localization-delocalization transition (LDT) and its critical properties. For M >= 3 the LDT exists and a normal diffusion is recovered above a critical strength epsilon, and the characteristics of diffusion dynamics mimic the diffusion process predicted for the stochastically perturbed Anderson model even though M is not large. These results are compared with the results of discrete-time quantum maps, i.e., the Anderson map and the standard map. Further, the features of delocalized dynamics are discussed in comparison with a limit model which has no static disordered part.