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On two non-ergodic reversible cellular automata, one classical, the other quantum
ID Prosen, Tomaž (Author)

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Abstract
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 ±1 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.

Language:English
Keywords:cellular automata, ergodicity, ergodicity breaking, integrability, dynamical systems
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication version:Version of Record
Publication date:30.04.2023
Year:2023
Number of pages:13 str.
Numbering:Vol. 25, iss. 5, art. no. 739
PID:20.500.12556/RUL-155493 This link opens in a new window
UDC:536.9
ISSN on article:1099-4300
DOI:10.3390/e25050739 This link opens in a new window
COBISS.SI-ID:191436035 This link opens in a new window
Publication date in RUL:04.04.2024
Views:279
Downloads:193
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Record is a part of a journal

Title:Entropy
Shortened title:Entropy
Publisher:MDPI
ISSN:1099-4300
COBISS.SI-ID:515806233 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.

Secondary language

Language:Slovenian
Keywords:celični avtomati, ergodičnost, zlom ergodičnosti, integrabilnost, dinamični sistemi

Projects

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0402-2019
Name:Matematična fizika

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0233-2022
Name:Dinamika v interagirajočih kvantnih mnogodelčnih sistemih

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0219-2022
Name:Kvantna ergodičnost: Stabilnost in Prehodi

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