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We introduce well-defined characterizations of prethermal states in realisticperiodically driven many-body systems with unbounded chaotic diffusion of thekinetic energy. These systems, interacting arrays of periodically kickedrotors, are paradigmatic models of many-body chaos theory. We show that theprethermal states in these systems are well described by a generalized Gibbsensemble based essentially on the average Hamiltonian. The latter is thequasi-conserved quantity in the prethermal state and the ensemble ischaracterized by the temperature of the state. An explicit exact expression forthis temperature is derived. Also, using arguments based on chaos theory, wedemonstrate that the lifetime of the prethermal state is exponentially long inthe inverse of the temperature. Our analytical results, in particular those forthe temperature and the lifetime of the prethermal state, agree well withnumerical observations.

Characterizations of prethermal states in periodically driven many-body systems with unbounded chaotic diffusion