Dynamical localization and the effects of aperiodicity in Floquet systems

TL;DR

This paper investigates how periodic and aperiodic driving in a 1D quantum system affects localization, revealing that aperiodicity leads to delocalization and diffusive wave packet spreading.

Contribution

It demonstrates the transition from dynamical localization to delocalization due to aperiodic modulations in Floquet systems, extending understanding of robustness of localization.

Findings

Periodic incommensurate modulations induce dynamical localization.

Aperiodic modulations cause delocalization and diffusive spreading.

Localization robustness diminishes with increasing aperiodicity.

Abstract

We study the localization aspects of a kicked non-interacting one-dimensional (1D) quantum system subject to either time-periodic or non-periodic pulses. These are reflected as sudden changes of the onsite energies in the lattice with different modulations in real space. When the modulation of the kick is incommensurate with the lattice spacing, and the kicks are periodic, a well known dynamical localization in real space is recovered for large kick amplitudes and frequencies. We explore the universality class of this transition and also test the robustness of localization under deviations from the perfect periodic case. We show that delocalization ultimately sets in and a diffusive spreading of an initial wave packet is obtained when the aperiodicity of the driving is introduced.