Space-like dynamics in a reversible cellular automaton

Katja Klobas (Author), Tomaž Prosen (Author)

Abstract

In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

Keywords

celični avtomati;cellular automata;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.2
COBISS:	42968579
ISSN:	2666-9366
Views:	408
Downloads:	291
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	celični avtomati;
Pages:	28 str.
Volume:	ǂVol. ǂ2
Issue:	ǂart. no. ǂ010
Chronology:	Jun. 2020
DOI:	10.21468/SciPostPhysCore.2.2.010
ID:	12345750