Exact solution of the "rule 150" reversible cellular automaton

Wilkinson, Joseph W.P.; Prosen, Tomaž; Garrahan, Juan P.

Abstract

We study the dynamics and statistics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics that corresponds to a bulk deterministic and reversible discretized version of the kinetically constrained "exclusive one-spin facilitated"(XOR) Fredrickson-Andersen (FA) model, where the local dynamics is restricted: A site flips if and only if its adjacent sites are in different states from each other. Similar to other RCA that have been recently studied, such as Rule 54 and Rule 201, the Rule 150 RCA is integrable, however, in contrast is noninteracting: The emergent quasiparticles, which are identified by the domain walls, behave as free fermions. This property allows us to solve the model by means of matrix product ansatz. In particular, we find the exact equilibrium and nonequilibrium stationary states for systems with closed (periodic) and open (stochastic) boundaries, respectively, resolve the full spectrum of the time evolution operator and, therefore, gain access to the relaxation dynamics, and obtain the exact large deviation statistics of dynamical observables in the long-time limit.

Citation

Wilkinson, J. W., Prosen, T., & Garrahan, J. P. (2022). Exact solution of the "rule 150" reversible cellular automaton. Physical Review E, 105(3), Article 034124. https://doi.org/10.1103/PhysRevE.105.034124

• Journal Article Type: Article
• Acceptance Date: Feb 18, 2022
• Online Publication Date: Mar 17, 2022
• Publication Date: 2022-03
• Deposit Date: Feb 21, 2022
• Publicly Available Date: Mar 17, 2022
• Journal: Physical Review E
• Print ISSN: 1539-3755
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 3
• Article Number: 034124
• DOI: https://doi.org/10.1103/PhysRevE.105.034124
• Public URL: https://nottingham-repository.worktribe.com/output/7501013
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.034124