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

Liu, S.-W., Willsher, J., Bilitewski, T., Li, J.-J., Smith, A., Christensen, K., et al. (2021). Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton. Physical Review B, 103(9): 094109. doi:10.1103/PhysRevB.103.094109.

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Liu, Shu-Wei1, Author           
Willsher, J.2, Author
Bilitewski, T.2, Author
Li, Jin-Jie2, Author
Smith, A.2, Author
Christensen, K.2, Author
Moessner, Roderich1, Author           
Knolle, J.2, Author
Affiliations:
1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              
2external, ou_persistent22              

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 MPIPKS: Deterministic dynamics
 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 lambda(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 v(b) and the exponent beta in the scaling ansatz lambda(v) similar to 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.

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 Dates: 2021-03-172021-03-01
 Publication Status: Issued
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Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 103 (9) Sequence Number: 094109 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008