Quantum diffusion in the Harper model under polychromatic time-perturbation

Abstract

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 $\hat{I}\mu$ increases for $M\ge 3$. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the $(\hat{I}\mu ,V)$ parameter space is presented.

13 pages, 19 figures