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Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here we show that, although any randomness in the interactions of a many-body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down (shoots up) by orders of magnitude as the ratio of the drive frequency and amplitude h₀ tends to certain specific values (the freezing condition). If is increased while maintaining the ratio h₀/ at a fixed freezing value, then diverges exponentially with. The results can be easily extended for a larger family of disordered fermionic and bosonic systems.
Roy et al. (Fri,) studied this question.