Quantum dynamics of the Harper model with self-duality exhibits localized, diffusive, and ballistic states depending on the potential strength $V$. By adding time-dependent harmonic perturbations composed of $M$ incommensurate frequencies, we show that all states of the Harper model transition to quantum diffusive states as the perturbation strength $\epsilon$ increases for $M\ge 3$. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the $(\epsilon ,V)$ parameter space is presented.

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• Ballistic transport
• Diffusion
• Dynamical phase transitions
• Hopping transport
• Localization
• Quantum chaos
• Quantum interference effects
• Quantum phase transitions