Suppressed heating and pre-thermalization in chains of classical kicked rotors

Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental question with important practical implications. We address this question by analyzing a chain of coupled kicked rotors, and find two situations in which the heating rate can be arbitrarily small: (i) marginal localization, for drives with large frequencies and small amplitudes, (ii) linear stability, for initial conditions close to a fixed point. In both cases, we find that the dynamics shows universal scaling laws that allow us to distinguish localized, diffusive, and super-diffusive regimes. The marginally localized phase has common traits with recently discovered pre-thermalized phases of many-body quantum-Hamiltonian systems, but does not require quantum coherence.