Quantum Lyapunov spectrum
Quantum Lyapunov spectrum
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DOI：
10.1007/jhep04(2019)082
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发表时间：
2019-04-10
影响因子：
5.4
通讯作者：
Tezuka, Masaki
中科院分区：
文献类型：
--
作者：
Gharibyan, Hrant;Hanada, Masanori;Tezuka, Masaki
我们介绍了一个简单的量子概括的经典李雅普诺夫指数的频谱。我们将其应用到SYK和XXZ模型中，研究了系统的Lyapunov增长和熵产生。我们的数值结果表明，黑洞不仅是最快的扰乱器，而且是最快的熵产生器。我们还研究了量子李雅普诺夫谱的统计特征，发现了普遍的随机矩阵行为，这类似于最近发现的经典混沌的普遍性。当系统变形远离混沌，朝向可积性或多体局域相时，随机矩阵行为丢失。我们提出，量子系统全息对偶引力满足这种普遍性的强形式。我们进一步认为，量子李雅普诺夫谱包含重要的额外信息以外的最大李雅普诺夫指数，从而为我们提供了一个更好的表征量子系统中的混沌。
We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.