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

Tomaž Prosen1

  • 1Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.

Entropy (Basel, Switzerland)
|May 27, 2023
PubMed
Summary
This summary is machine-generated.

We introduce two simple kinetic particle models with unique properties. One model reveals non-ergodic behavior and potential integrability, while the other generates infinite conserved operators called glider operators.

Keywords:
cellular automataconservation lawsergodic theoryergodicity breakingintegrabilityinteracting dynamics

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Cellular automata offer simplified models for complex physical systems.
  • Kinetic particle models are crucial for understanding emergent phenomena.
  • Lattice gas models provide insights into fluid dynamics and statistical properties.

Purpose of the Study:

  • To propose and analyze two novel 1+1 dimensional kinetic particle models.
  • To explore the properties of deterministic, reversible automata and their conserved quantities.
  • To investigate a quantum deformation of a charged hardpoint lattice gas and its conserved operators.

Main Methods:

  • Development of two cellular automaton models with distinct particle types and interactions.
  • Analysis of continuity equations to identify conserved charges and currents.
  • Investigation of the Yang-Baxter equation and related identities for quantum deformations.

Main Results:

  • The first model exhibits three conserved charges, with one charge and current of nine-site support, indicating non-ergodicity and potential integrability.
  • The second model, a quantum deformation, satisfies a Yang-Baxter related identity, leading to an infinite set of glider operators.
  • Both models demonstrate intriguing properties suitable for further research and applications.

Conclusions:

  • The proposed kinetic particle models offer simplified yet powerful frameworks for studying complex systems.
  • The discovery of non-ergodic behavior and infinite conserved operators highlights the potential for novel applications.
  • These models warrant further investigation into their mathematical structures and physical implications.