Rozenbaum Efim B, Bunimovich Leonid A, Galitski Victor
Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2020 Jul 3;125(1):014101. doi: 10.1103/PhysRevLett.125.014101.
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.
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在随后会产生指数级的巨大影响。但这种现象很难与量子力学相协调。量子混沌领域的主要目标之一是在经典混沌系统及其量子对应物的动力学之间建立一种对应关系。在没有退相干的孤立系统中，动力学中存在这样一种对应关系，但它通常只在短时间窗口内持续，之后量子干涉会消除经典混沌。我们证明，在这个早期窗口内，量子力学也可以起到相反的作用，并在经典非混沌系统中产生指数不稳定性。我们的计算采用了时间反序关联函数（OTOC）——一种在经典极限下简化为李雅普诺夫指数但对一般量子系统也有明确定义的诊断工具。我们表明，某些经典非混沌模型，如多边形台球，在早期会以与普朗克常数相关的速率表现出OTOC类似李雅普诺夫指数的增长。这种行为与系统经典对应物中OTOC类似物早期的缓慢增长形成鲜明对比。这些结果表明，即使在量子干涉出现之前，动力学中的经典到量子对应关系在OTOC中就已经被打破。
