Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton
Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton
复制标题
混沌元胞自动机中信息传播的蝴蝶效应和空间结构
作者：
Shuwei Liu;Josef Willsher;T. Bilitewski;Jinjie Li;A. Smith;K. Christensen;R. Moessner;J. Knolle
Inspired by recent developments in the study of chaos in many-body systems, we construct a measure of local information spreading for a stochastic Cellular Automaton in the form of a spatiotemporally resolved Hamming distance. This decorrelator is a classical version of an Out-of-Time-Order Correlator studied in the context of quantum many-body systems. Focusing on the one-dimensional Kauffman Cellular Automaton, we extract the scaling form of our decorrelator with an associated butterfly velocity $v_b$ and a velocity-dependent Lyapunov exponent $\lambda(v)$. The existence of the latter is not a given in a discrete classical system. Second, we account for the behaviour of the decorrelator in a framework based solely on the boundary of the information spreading, including an effective boundary random walk model yielding the full functional form of the decorrelator. In particular, we obtain analytic results for $v_b$ and the exponent $\beta$ in the scaling ansatz $\lambda(v) \sim \mu (v - v_b)^\beta$, which is usually only obtained numerically. Finally, a full scaling collapse establishes the decorrelator as a unifying diagnostic of information spreading.
