We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite temperature--spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterised by the Lyapunov exponents and the butterfly speed respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analysing the scaling forms, we relate the growth, spread and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang (KPZ) equation.

中文翻译：

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经典自旋链中光锥的扰动传播和蝴蝶效应

我们发现，即使局部自旋动力学具有扩散性，在混沌古典多体系统（无限温度下的经典海森堡链）中，局部扰动的影响也会以有限的速度弹道扩展。我们研究了这种蝴蝶效应的两个互补方面：摄动的快速增长及其同时的弹道（光锥）传播，分别以李雅普诺夫指数和蝴蝶速度为特征。我们将此与最近对无序换向器（OTOC）的研究相联系，该研究已被建议作为量子系统中混沌的指标。我们使用系统中的自然相关器对OTOC进行了直接鉴定，并证明了经典系统中存在许多有趣的定性特征。最后，