Quantum diffusion in the Harper model under polychromatic time-perturbation

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 $ε$ increases for $M \geq 3$. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the $(ε,V)$ parameter space is presented.