On two reversible cellular automata with two particle species

Katja Klobas*, Tomaz Prosen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

We introduce a pair of time-reversible models defined on the discrete space-time lattice with three states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P), and time-reversal (T) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the hydrodynamic prediction for the model with exactly three local charges. Surprisingly, the numerically observed 'sound velocity' does not match the hydrodynamic value. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.

Original languageEnglish
Article number094003
Number of pages26
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number9
Early online date21 Feb 2022
DOIs
Publication statusPublished - 4 Mar 2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.

Keywords

  • cellular automata
  • classical dynamics
  • correlation functions
  • equilibration
  • hydrodynamics
  • transport

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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