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Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems
Physical Review Letters ( IF 8.6 ) Pub Date : 2021-07-30 , DOI: 10.1103/physrevlett.127.050602
Takashi Mori 1 , Hongzheng Zhao 2 , Florian Mintert 2 , Johannes Knolle 2, 3, 4 , Roderich Moessner 5
Affiliation  

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 aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic 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 quasiperiodic driving suggests that the heating time scales like (ω/g)Cln(ω/g) with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.

中文翻译:

Thue-Morse 准周期和随机驱动的量子多体系统中加热速率的严格界限

封闭多体系统的非平衡量子动力​​学是一个丰富而具有挑战性的领域。虽然最近周期性驱动(Floquet)系统的进展已经产生了许多严格的结果,但我们对由快速变化但非周期性和准周期性驱动驱动的量子多体系统的理解仍然有限。在这里,我们推导出了在 Thue-Morse 准周期驱动和随机多极驱动下的量子多体系统中加热速率的严格的、非微扰的界限,后者是前者的可调谐随机变体。在这个过程中,我们推导出了一个静态有效哈密顿量,它描述了瞬态热前状态,包括局部可观测量的动力学。我们对 Thue-Morse 准周期驱动的界限表明加热时间的尺度如下(ω/G)-C输入(ω/G) 具有正常数 C 和典型的能量等级 G 的哈密顿量,与我们的数值模拟一致。
更新日期:2021-07-30
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