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

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 $M\ge 2$ 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 $M\ge 3$. 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 $\eps$.

11 pages, 14 figures

References in corpus (12)

• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Experimental Realization of Quantum-Resonance Ratchets
• Rectified momentum transport for a kicked Bose-Einstein Condensate
• Drive Induced Delocalization in Aubry-André Model
• From localization to anomalous diffusion in the dynamics of coupled kicked rotors
• Dynamical localization and the effects of aperiodicity in Floquet systems
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Quantum Computation of a Complex System : the Kicked Harper Model
• Controlled decoherence in a quantum Lévy kicked rotator
• Single-particle localization in dynamical potentials
• Dynamical transitions in aperiodically kicked tight-binding models
• Critical Phenomena of Dynamical Delocalization in Quantum Maps:standard map and Anderson map