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

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.