Related papers: Integrability breaking in the Rule 54 cellular aut…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…
We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54". For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in…
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…
A family of reversible deterministic cellular automata, including the rules 54 and 201 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] as well as their kinetically constrained quantum (unitary) or stochastic deformations, is shown…
We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional…
The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its…
We review recent results on an exactly solvable model of nonequilibrium statistical mechanics, specifically the classical Rule 54 reversible cellular automaton and some of its quantum extensions. We discuss the exact microscopic description…
Precipitation/dissolution reactions coupled with solute transport are modelled as a cellular automaton in which solute molecules perform a random walk on a regular lattice and react according to a local probabilistic rule. Stationary solid…
Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for complete integrability. This severely constrains their dynamical processes, and it often leads to their exact…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and…
We study quantum and stochastic deformations of the rule-54 reversible cellular automaton (RCA54) on a 1+1-dimensional spatiotemporal lattice, focusing on their integrability structures in two distinct settings. First, for the quantum…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
In a many-body quantum system, local operators in Heisenberg picture $O(t) = e^{i H t} O e^{-i H t}$ spread as time increases. Recent studies have attempted to find features of that spreading which could distinguish between chaotic and…
We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…