Localization and delocalization properties in quasi-periodically perturbed Kicked Harper and Harper models

TL;DR

This paper numerically investigates localization and delocalization phenomena in kicked Harper and Harper models under quasi-periodic perturbations, revealing conditions for transitions and diffusive behaviors in wave packet dynamics.

Contribution

It provides new insights into how quasi-periodic perturbations induce localization-delocalization transitions in these models, with detailed analysis of the critical perturbation strength and diffusive properties.

Findings

Localization persists for M=1 in both models.

LDT occurs for M≥2 in KHM and M≥3 in Harper model.

Ballistic to diffusive transition observed above critical perturbation strength.

Abstract

We numerically study the single particle localization and delocalization phenomena of an initially localized wave packet in the kicked Harper model (KHM) and Harper model subjected to quasi-periodic perturbation composed of $M-$modes. Both models are localized in the monochromatically perturbed case $M=1$. KHM shows localization-delocalization transition (LDT) above $M\geq2$ as increase of the perturbation strength $\eps$. In contrast, in a time-continuous Harper model with the perturbation, it is confirmed that the localization persists for $M=2$ and the LDT occurs for $M\geq 3$. Furthermore, we investigate the diffusive property of the delocalized wave packet in the KHM and Harper model for $\eps$ above the critical strength $\eps_c$ ($\eps>\eps_c$) comparing with other type systems without localization, which takes place a ballistic to diffusive transition in the wave packet dynamics as the increase of $\eps$.