We study the localization aspects of a kicked noninteracting one-dimensional (1D) quantum system subject to either time-periodic or nonperiodic pulses. These are reflected as sudden changes of the on-site 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.

• Received 24 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.144301