Space-like dynamics in a reversible cellular automaton

Klobas, Katja (avtor), Prosen, Tomaž (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: cellular automata
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2020
• Št. strani: 28 str.
• Številčenje: Vol. 2, art. no. 010
• PID: 20.500.12556/RUL-124025
• UDK: 519.2
• ISSN pri članku: 2666-9366
• DOI: 10.21468/SciPostPhysCore.2.2.010
• COBISS.SI-ID: 42968579
• Datum objave v RUL: 21.12.2020

Gradivo je del revije

• Naslov: SciPost physics core
• Založnik: SciPost Foundation
• ISSN: 2666-9366
• COBISS.SI-ID: 18961667

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
• Začetek licenciranja: 21.12.2020

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: celični avtomati

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open Many-body Non-Equilibrium Systems
• Akronim: OMNES

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika