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Space-like dynamics in a reversible cellular automaton
ID Klobas, Katja (Author), ID Prosen, Tomaž (Author)

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Abstract
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 This link opens in a new window
UDC:519.2
ISSN on article:2666-9366
DOI:10.21468/SciPostPhysCore.2.2.010 This link opens in a new window
COBISS.SI-ID:42968579 This link opens in a new window
Publication date in RUL:21.12.2020
Views:1307
Downloads:456
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Record is a part of a journal

Title:SciPost physics core
Publisher:SciPost Foundation
ISSN:2666-9366
COBISS.SI-ID:18961667 This link opens in a new window

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

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