From prethermalization to chaos in periodically driven coupled rotors

Periodically driven (Floquet) systems are said to prethermalize when their energy absorption is very slow for a long time. This effect was first discovered in quantum spin models, where the heating rate is exponentially small in the ratio between the driving frequency and the spin bandwidth. Recently, it was shown that prethermalization occurs also in classical systems with an infinite bandwidth. Here, we address the open question of which small parameter controls the lifetime of the prethermal state in these systems. We show that the lifetime is controlled by the temperature of the prethermal state, which is quasiconserved when the heating is slow. We substantiate this finding in systems of periodically driven coupled rotors, by studying the dependence of the prethermal lifetime on both the initial conditions and the connectivity. This result allows us to develop a simple analytical model that describes the crossover from prethermalization to chaos in many-body classical systems.