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Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton

Liu, Shu-Wei; Willsher, J.; Bilitewski, T.; Li, Jin-Jie; Smith, A.; Christensen, K.; Moessner, R.; Knolle, J.

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Authors

Shu-Wei Liu

J. Willsher

T. Bilitewski

Jin-Jie Li

K. Christensen

R. Moessner

J. Knolle



Abstract

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 vb and a velocity-dependent Lyapunov exponent λ(v). The existence of the latter is not a given in a discrete classical system. Second, we account for the behavior 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 vb and the exponent β in the scaling ansatz λ(v)∼μ(v−vb)β, which is usually only obtained numerically. Finally, a full scaling collapse establishes the decorrelator as a unifying diagnostic of information spreading.

Citation

Liu, S., Willsher, J., Bilitewski, T., Li, J., Smith, A., Christensen, K., …Knolle, J. (2021). Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton. Physical Review B, 103(9), Article 094109. https://doi.org/10.1103/physrevb.103.094109

Journal Article Type Article
Acceptance Date Mar 8, 2021
Online Publication Date Mar 17, 2021
Publication Date Mar 1, 2021
Deposit Date Jun 17, 2021
Publicly Available Date Jun 17, 2021
Journal Physical Review B
Print ISSN 2469-9950
Electronic ISSN 2469-9969
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 103
Issue 9
Article Number 094109
DOI https://doi.org/10.1103/physrevb.103.094109
Public URL https://nottingham-repository.worktribe.com/output/5689796
Publisher URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.094109

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