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On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †

We propose and discuss two variants of kinetic particle models—cellular automata in 1 + 1 dimensions—that have some appeal due to their simplicity and intriguing properties, which could warrant further research and applications. The first model is a deterministic and reversible automaton describing...

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Autor principal: Prosen, Tomaž
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217703/
https://www.ncbi.nlm.nih.gov/pubmed/37238494
http://dx.doi.org/10.3390/e25050739
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author Prosen, Tomaž
author_facet Prosen, Tomaž
author_sort Prosen, Tomaž
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description We propose and discuss two variants of kinetic particle models—cellular automata in 1 + 1 dimensions—that have some appeal due to their simplicity and intriguing properties, which could warrant further research and applications. The first model is a deterministic and reversible automaton describing two species of quasiparticles: stable massless matter particles moving with velocity [Formula: see text] and unstable standing (zero velocity) field particles. We discuss two distinct continuity equations for three conserved charges of the model. While the first two charges and the corresponding currents have support of three lattice sites and represent a lattice analogue of the conserved energy–momentum tensor, we find an additional conserved charge and current with support of nine sites, implying non-ergodic behaviour and potentially signalling integrability of the model with a highly nested R-matrix structure. The second model represents a quantum (or stochastic) deformation of a recently introduced and studied charged hardpoint lattice gas, where particles of different binary charge (±1) and binary velocity (±1) can nontrivially mix upon elastic collisional scattering. We show that while the unitary evolution rule of this model does not satisfy the full Yang–Baxter equation, it still satisfies an intriguing related identity which gives birth to an infinite set of local conserved operators, the so-called glider operators.
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spelling pubmed-102177032023-05-27 On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum † Prosen, Tomaž Entropy (Basel) Article We propose and discuss two variants of kinetic particle models—cellular automata in 1 + 1 dimensions—that have some appeal due to their simplicity and intriguing properties, which could warrant further research and applications. The first model is a deterministic and reversible automaton describing two species of quasiparticles: stable massless matter particles moving with velocity [Formula: see text] and unstable standing (zero velocity) field particles. We discuss two distinct continuity equations for three conserved charges of the model. While the first two charges and the corresponding currents have support of three lattice sites and represent a lattice analogue of the conserved energy–momentum tensor, we find an additional conserved charge and current with support of nine sites, implying non-ergodic behaviour and potentially signalling integrability of the model with a highly nested R-matrix structure. The second model represents a quantum (or stochastic) deformation of a recently introduced and studied charged hardpoint lattice gas, where particles of different binary charge (±1) and binary velocity (±1) can nontrivially mix upon elastic collisional scattering. We show that while the unitary evolution rule of this model does not satisfy the full Yang–Baxter equation, it still satisfies an intriguing related identity which gives birth to an infinite set of local conserved operators, the so-called glider operators. MDPI 2023-04-30 /pmc/articles/PMC10217703/ /pubmed/37238494 http://dx.doi.org/10.3390/e25050739 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Prosen, Tomaž
On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title_full On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title_fullStr On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title_full_unstemmed On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title_short On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum †
title_sort on two non-ergodic reversible cellular automata, one classical, the other quantum †
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217703/
https://www.ncbi.nlm.nih.gov/pubmed/37238494
http://dx.doi.org/10.3390/e25050739
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