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≥3. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the (ε,V) parameter space is presented.