Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

Abstract

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but a- and quasi-periodic driving is still limited. Here, we derive rigorous, non-perturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasi-periodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasi-periodic driving suggests that the heating time scales like $(\omega /g{)}^{-C\ln (\omega /g)}$ with a positive constant $C$ and a typical energy scale $g$ of the Hamiltonian, in agreement with our numerical simulations.

arXiv comment5+6 pages, 2 figures

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• Localization persisting under aperiodic driving
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• Prethermalization in aperiodically driven classical spin systems
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• Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor
• Critically Slow Hilbert-Space Ergodicity in Quantum Morphic Drives
• Floquet-engineered Emergent Massive Nambu-Goldstone Modes
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Engineering Hierarchical Symmetries
• Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model
• Stable time rondeau crystals in dissipative many-body systems
• Statistical prethermalization in randomly kicked many-body classical rotor system
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