Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model
Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model
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DOI：
10.1103/physrevb.99.134301
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发表时间：
2018-02
影响因子：
3.7
通讯作者：
M. Schmitt;Dries Sels;S. Kehrein;A. Polkovnikov
中科院分区：
文献类型：
--
作者：
M. Schmitt;Dries Sels;S. Kehrein;A. Polkovnikov
量子蝴蝶效应对小扰动的指数敏感性的存在已经争论了很长时间。最近，这个问题已经获得了越来越多的兴趣，由于建议探测混沌动力学和扰码使用的时间顺序的干扰器。在这项工作中，我们研究了回声动力学的Sachdev-Ye-Kitaev模型下的有效时间反演在半经典的方法，使用截断的维格纳近似，这占非零量子波动的动力学是必不可少的。我们证明，在时间反演过程中引入的小缺陷导致从完美的回波的指数发散，这使我们能够识别李雅普诺夫指数${\ensuremath{\lambda}}_{L}$。特别地，我们发现${\ensuremath{\lambda}}_{L}$是半经典运动方程的李雅普诺夫指数的两倍。这种行为归因于一个无序的时间顺序双换向器，类似于一个无序的时间顺序相关的增长。
The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question has gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators. In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach using the truncated Wigner approximation, which accounts for nonvanishing quantum fluctuations that are essential for the dynamics. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows us to identify a Lyapunov exponent ${\ensuremath{\lambda}}_{L}$. In particular, we find that ${\ensuremath{\lambda}}_{L}$ is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator.