Localization and delocalization properties in quasi-periodically perturbed Kicked Harper and Harper models

Abstract

We numerically study the single particle localization and delocalization phenomena of an initially localized wave packet in the kicked Harper model (KHM) and Harper model subjected to quasiperiodic perturbation composed of M −modes. Both models are localized in the monochromatically perturbed case M = 1. KHM shows localization-delocalization transition (LDT) above M ≥ 2 as increase of the perturbation strength ǫ. In a time-continuous Harper model with the perturbation, it is confirmed that the localization persists for M = 2 and the LDT occurs for M ≥ 3. In addition, we investigate the diffusive property of the delocalized wave packet for ǫ above the critical strength ǫc (ǫ > ǫc). We also introduce other type systems without localization, which takes place a ballistic to diffusive transition in the wave packet dynamics as the increase of ǫ. In both systems, the ǫ−dependence of the diffusion coefficient well coincide with that in the other type system for large ǫ(> 1).