论文标题
没有混乱的超级相关器的指数增长：倒谐波振荡器
Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
论文作者
论文摘要
我们提供了对无混乱的系统中的及时生长的热阶外阶（OTOC）的详细检查。该系统是一种一维量子力学，具有势为倒谐波振荡器的电势。当温度高于一定阈值时，我们从数值上观察OTOC的指数生长。发现Lyapunov指数是在山顶生成的经典Lyapunov指数的顺序，即使在高温下，它仍然不存在。我们采用各种潜力形状，并找到这些特征通用。该研究证实，当电势包括局部最大值时，热OTOC的指数生长不一定意味着混乱。我们还为在一个维度的通用量子力学中为热OTOC的Lyapunov指数提供了界限，该量子的形式与Maldacena，Shenker和Stanford获得的混乱形式相同。
We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.
