The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

中文翻译：

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Bose-Hubbard 模型的统计 Floquet 预热化

多体系统的操纵通常涉及导致不必要加热的时间相关力。抑制加热的一种策略是在大驱动频率下使用时间周期 (Floquet) 力。对于具有有界光谱的量子自旋系统，严格证明加热速率在驱动频率中呈指数级小。最近，在超冷原子实验中也观察到了加热的指数抑制，实现了周期性驱动的 Bose-Hubbard 模型。该模型具有无限的频谱，因此超出了以前的理论方法的范围。在这里，我们用两种半经典方法研究这个模型，分别在大相互作用强度和弱相互作用强度下有效。在这两个限制中，我们通过研究遇到多体共振的统计概率来计算加热速率，并获得与量子模型的精确对角化的定量一致。我们的方法证明了统计参数与相互作用的多体量子系统的 Floquet 过热化的相关性。