Dynamical Localization and Delocalization in Floquet Systems*

We study the localization aspects of a kicked noninteracting one-dimensional quantum system of spinless fermions and a topological superconductor subject to either time-periodic or aperiodic pulses. The universality class of the transition from delocalized to localized regimes is studied in the case of time-periodic and spatially quasi-periodic kicks. In the case of aperiodic kicks, delocalization ultimately sets in and a diffusive spreading of an initial wave packet is obtained even for small time-aperiodicity of the driving. In the case of Floquet topological superconductors, one finds both Majorana and fermionic localized edge modes in the topological regime. In the intermediate driving period regime, one can identify a region in the phase diagram with a mobility edge between critical and localized states. Finally, we analyze the robustness of the Majorana modes to deviations on the driving period, finding they are stable in a small set of the parameters.