Quantum diffusion in the Harper model under polychromatic time-perturbation

TL;DR

This paper investigates how adding multiple incommensurate harmonic perturbations to the Harper model induces a transition from localized, diffusive, or ballistic states to quantum diffusive states across all potential strengths, revealing complex phase behavior.

Contribution

It demonstrates that in the Harper model with self-duality, multi-frequency time perturbations cause a universal transition to diffusive states for sufficiently strong perturbations.

Findings

All states become diffusive with increasing perturbation strength for M ≥ 3.

The phase diagram in (ε,V) space maps the transition regions.

Diffusive behavior depends on the number of incommensurate frequencies.

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