  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 $1<\alpha<2$.
