The majority of classical dynamical systems are chaotic and exhibit the butterfly effect: a minute change in initial conditions has exponentially large effects later on. But this phenomenon is difficult to reconcile with quantum mechanics. One of the main goals in the field of quantum chaos is to establish a correspondence between the dynamics of classical chaotic systems and their quantum counterparts. In isolated systems in the absence of decoherence, there is such a correspondence in dynamics, but it usually persists only over a short time window, after which quantum interference washes out classical chaos. We demonstrate that quantum mechanics can also play the opposite role and generate exponential instabilities in classically nonchaotic systems within this early-time window. Our calculations employ the out-of-time-ordered correlator (OTOC)—a diagnostic that reduces to the Lyapunov exponent in the classical limit but is well defined for general quantum systems. We show that certain classically nonchaotic models, such as polygonal billiards, demonstrate a Lyapunov-like exponential growth of the OTOC at early times with Planck’s-constant-dependent rates. This behavior is sharply contrasted with the slow early-time growth of the analog of the OTOC in the systems’ classical counterparts. These results suggest that classical-to-quantum correspondence in dynamics is violated in the OTOC even before quantum interference develops.

中文翻译：

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非混沌量子系统中的早期指数不稳定性。

大多数经典动力学系统都是混沌的，并表现出蝴蝶效应：初始条件的微小变化随后会产生指数级的巨大影响。但是这种现象很难与量子力学调和。量子混沌领域的主要目标之一是在经典混沌系统的动力学及其量子对应物之间建立对应关系。在没有退相干的孤立系统中，动力学上存在这种对应关系，但通常仅在很短的时间范围内持续存在，此后量子干扰将消除经典的混乱。我们证明了量子力学还可以在这个早期窗口内在经典的非混沌系统中发挥相反的作用并产生指数不稳定性。我们的计算使用了无序相关器（OTOC），这是一种诊断方法，可以在经典极限条件下降低到Lyapunov指数，但对于一般的量子系统已得到很好的定义。我们表明，某些经典的非混沌模型（例如多边形台球）在早期以普朗克恒定速率显示了OTOC的Lyapunov样指数增长。与传统系统中OTOC类似物的早期缓慢增长形成鲜明对比。这些结果表明，甚至在量子干扰发展之前，OTOC中就已经违反了动力学中经典与量子的对应关系。例如多边形台球，在普朗克常数依赖的速率下，展现了OTOC早期Lyapunov状的指数增长。与传统系统中OTOC类似物的早期缓慢增长形成鲜明对比。这些结果表明，甚至在量子干扰发展之前，OTOC中就已经违反了动力学中经典与量子的对应关系。例如多边形台球，在早期以普朗克常数依赖性速率显示了OTOC的Lyapunov状指数增长。与传统系统中OTOC类似物的早期缓慢增长形成鲜明对比。这些结果表明，甚至在量子干扰发展之前，OTOC中就已经违反了动力学中经典与量子的对应关系。