Effect of temporal disorder on wave packet dynamics in one-dimensional kicked lattices

Inspired by the recent experimental progress in noisy kicked rotor systems, we investigate the effect of temporal disorder or quasi-periodicity in one-dimensional kicked lattices with pulsed on-site potential. We found that, unlike the spatial disorder or quasi-periodicity which usually leads to localization, the effect of the temporal one is more complex and depends on the spatial configuration. If the kicked on-site potential is periodic in real space, then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity. On the other hand, if the kicked on-site potential is spatially quasi-periodic, then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range. The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization.