Space-like dynamics in a reversible cellular automaton

Klobas, Katja (author), Prosen, Tomaž (author)

In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

• Language: English
• Keywords: cellular automata
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: 28 str.
• Numbering: Vol. 2, art. no. 010
• PID: 20.500.12556/RUL-124025
• UDC: 519.2
• ISSN on article: 2666-9366
• DOI: 10.21468/SciPostPhysCore.2.2.010
• COBISS.SI-ID: 42968579
• Publication date in RUL: 21.12.2020

KLOBAS, Katja and PROSEN, Tomaž, 2020, Space-like dynamics in a reversible cellular automaton. SciPost physics core [online]. 2020. Vol. 2, no. 010. [Accessed 24 March 2025]. DOI 10.21468/SciPostPhysCore.2.2.010. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=124025

Record is a part of a journal

• Title: SciPost physics core
• Publisher: SciPost Foundation
• ISSN: 2666-9366
• COBISS.SI-ID: 18961667

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.
• Licensing start date: 21.12.2020

Secondary language

• Language: Slovenian
• Keywords: celični avtomati

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika