Stability and pre-thermalization in chains of classical kicked rotors

Abstract

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) linear stability, for initial conditions close to a fixed point, and (ii) marginal localization, for drives with large frequencies and small amplitudes. In both cases, we find that the dynamics shows universal scaling laws that allow us to distinguish localized, diffusive, and sub-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.

21 single-column pages, 13 figures

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• Characterizations of prethermal states in periodically driven many-body systems with unbounded chaotic diffusion
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
• Bridging the gap between classical and quantum many-body information dynamics
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• Slow heating in a quantum coupled kicked rotors system
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• Stability, Isolated Chaos, and Superdiffusion in Nonequilibrium Many-Body Interacting Systems
• Statistical prethermalization in randomly kicked many-body classical rotor system
• Statistical Floquet prethermalization of the Bose-Hubbard model