Ergodic behaviors in reversible 3-state cellular automata

Sharipov, Rustem (author), Koterle, Matija (author), Grozdanov, Sašo (author), Prosen, Tomaž (author)

Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of ergodic behavior, we perform a systematic study of three-state cellular automata (with a stable ‘vacuum’ state and “particles” with $\pm$ charges). The classification is aided by the automata's different transformation properties under discrete symmetries: charge conjugation, spatial parity and time reversal. In particular, we propose a simple classification that distinguishes between types and levels of ergodic behavior in such system as quantified by the following observables: the mean return time, the number of conserved quantities, and the scaling of correlation functions. In each of the physically distinct classes, we present examples and discuss some of their phenomenology. This includes chaotic or ergodic dynamics, phase-space fragmentation, Ruelle-Pollicott resonances, existence of quasilocal charges, and anomalous transport with a variety of dynamical exponents.

• Language: English
• Keywords: quantum chaos, cellular automata, integrability
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 56 str.
• Numbering: Vol. 20, iss. 5
• PID: 20.500.12556/RUL-182822
• UDC: 530.145
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.20.5.145
• COBISS.SI-ID: 279196931
• Publication date in RUL: 25.05.2026

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kvantni kaos, celični avtomati, integrabilnost