Many-body energy localization transition in periodically driven systems

• A dynamical localization transition in periodically driven ergodic systems is found.
• This phenomenon is reminiscent of many-body localization in energy space.
• Our results are valid for classical and quantum systems in the thermodynamic limit.
• At critical frequency, the short time expansion for the evolution operator breaks down.
• The transition is associated to a divergent time scale.

According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space.