We study the survival of the current induced initially by applying a twist at the boundary of a chain of hard-core bosons (HCBs), subject to a periodic double $delta$-function kicks in the staggered on-site potential. We study the current flow and the work-done on the system at the long-time limit as a function of the driving frequency. Like a recent observation in the HCB chain with single $delta$-function kick in the staggered on-site potential, here we also observe many dips in the current flow and concurrently many peaks in the work-done on the system at some specific values of the driving frequency. However, unlike the single kicked case, here we do not observe a complete disappearance of the current in the limit of a high driving frequency, which shows the absence of any dynamical localization in the double $delta$-functions kicked HCB chain. Our analytical estimations of the saturated current and the saturated work-done, defined at the limit of a large time together with a high driving frequency, match very well with the exact numerics. In the case of the very small initial current, induced by a very small twist $ u$, we observe that the saturated current is proportional to $ u$. Finally, we study the time-evolution of the half-filled HCB chain where the particles are localized in the central part of the chain. We observe that the particles spread linearly in a light-cone like region at the rate determined by the maximum value of the group velocity. Except for a very trivial case, the maximum group velocity never vanishes, and therefore we do not observe any dynamical localization in the system.
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