Localized-Diffusive and Ballistic-Diffusive Transitions in Kicked Incommensurate lattice

By using the kicked Harper model, the effect of dynamical perturbations to the localized and ballistic phases in aperiodic lattice systems is investigated. The transition from the localized phase to diffusive phase via a critical sub-diffusion $t^{\alpha }$($t$:time) with $0<\alpha <1$ is observed. In addition, we first confirmed the existence of the transition from the ballistic phase to the diffusive phase via a critical super-diffusion with $1<\alpha <2$.