Applications of Temperley-Lieb algebras to Lorentz lattice gases
M.J. Martins, B. Nienhuis
TL;DR
This paper introduces a new algebraic framework based on Temperley-Lieb algebras to analyze the diffusive behavior of Lorentz lattice gases, providing solutions to the Yang-Baxter equation and exact geometrical scaling results.
Contribution
It develops a novel algebraic approach connecting Temperley-Lieb algebras with Lorentz lattice gases, enabling new insights into their diffusive properties.
Findings
Three classes of solutions to the Yang-Baxter equation identified
Exact geometrical scaling behavior of closed paths established
Framework facilitates analysis of diffusive dynamics in lattice gases
Abstract
Motived by the study of motion in a random environment we introduce and investigate a variant of the Temperley-Lieb algebra. This algebra is very rich, providing us three classes of solutions of the Yang-Baxter equation. This allows us to establish a theoretical framework to study the diffusive behaviour of a Lorentz Lattice gas. Exact results for the geometrical scaling behaviour of closed paths are also presented.
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