Free lunch served at 12:00

A periodically-driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent preprint, arXiv:1506.05455, Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study a non-integrable model of coupled quantum relativistic kicked rotors. We find that the interacting model exhibits dynamical localization in certain parameter regimes, which arises due to a complicated interplay of genuine Anderson mechanism and limiting integrable dynamics. This analysis of coupled "kicked" Dirac equations indicates that dynamical few- and many-body localization can exist in non-integrable systems and as such represents a generic phenomenon. We also analyze quantum dynamics of the model, which for certain model's parameters exhibits highly unusual behavior - e.g., superballistic transport and peculiar spin dynamics.