Localized-Diffusive and Ballistic-Diffusive Transitions in Kicked Incommensurate lattice

TL;DR

This paper investigates how dynamical perturbations affect phase transitions in aperiodic lattice systems using the kicked Harper model, revealing transitions from localized and ballistic phases to diffusive phases with critical sub-diffusion and super-diffusion behaviors.

Contribution

It demonstrates the existence of phase transitions from localized and ballistic to diffusive phases, including the first confirmation of super-diffusive transition in such systems.

Findings

Transition from localized to diffusive phase with sub-diffusion behavior.

Transition from ballistic to diffusive phase with super-diffusion behavior.

Identification of critical diffusion exponents in aperiodic lattice systems.

Abstract

By using the kicked Harper model, the effect of dynamical perturbations to the localized and ballistic phases in aperiodic lattice systems is investigated. The transition from the localized phase to diffusive phase via a critical sub-diffusion $t^\alpha$($t$:time) with $0<\alpha<1$ is observed. In addition, we first confirmed the existence of the transition from the ballistic phase to the diffusive phase via a critical super-diffusion with $1<\alpha<2$.