Space-like dynamics in a reversible cellular automaton

Katja Klobas (Avtor), Tomaž Prosen (Avtor)

Povzetek

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.

Ključne besede

celični avtomati;cellular automata;

Podatki

Jezik:	Angleški jezik
Leto izida:	2020
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	519.2
COBISS:	42968579
ISSN:	2666-9366
Št. ogledov:	408
Št. prenosov:	291
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	celični avtomati;
Strani:	28 str.
Letnik:	ǂVol. ǂ2
Zvezek:	ǂart. no. ǂ010
Čas izdaje:	Jun. 2020
DOI:	10.21468/SciPostPhysCore.2.2.010
ID:	12345750