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

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• Localization
• Quantum chaos
• Quantum phase transitions
• Quantum transport