Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalization in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator of chaos in quantum systems, despite the fact that saddle points in integrable systems can also drive rapid growth in OTOCs. By analyzing the Dicke model and a driven Bose-Hubbard dimer, we demonstrate that the OTOC growth driven by chaos can, nonetheless, be distinguished from that driven by saddle points through the long-term behavior. Besides quantitative differences in the long-term average, the saddle point gives rise to large oscillations not observed in the chaotic case. The differences are also highlighted by entanglement entropy, which in the chaotic-driven dimer matches a Page curve prediction. These results illustrate additional markers that can be used to distinguish chaotic behavior in quantum systems, beyond the initial exponential growth in OTOCs.

中文翻译：

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没有热化的鞍点加扰

失序相关器（OTOC）已被证明是研究量子系统中热化的有用工具。尤其是，尽管可积系统中的鞍点也可以推动OTOC的快速增长，但OTOCS的指数增长或加扰有时被视为量子系统混乱的指标。通过分析Dicke模型和受驱动的Bose-Hubbard二聚体，我们证明了通过长期行为，由混沌驱动的OTOC增长可与由鞍点驱动的增长区分开。除了长期平均值的数量差异外，鞍点还会引起在混沌情况下未观察到的大振荡。纠缠熵也突出了差异，纠缠熵在混沌驱动的二聚体中与Page曲线预测相匹配。