Exact matrix product decay modes of a boundary driven cellular automaton

Tomaž Prosen (Avtor), Berislav Buča (Avtor)

Povzetek

We study integrability properties of a reversible deterministic cellular automaton (Rule 54 of (Bobenko et al 1993 Commun. Math. Phys. 158 127)) and present a bulk algebraic relation and its inhomogeneous extension which allow for an explicit construction of Liouvillian decay modes for two distinct families of stochastic boundary driving. The spectrum of the many-body stochastic matrix defining the time propagation is found to separate into sets, which we call orbitals, and the eigenvalues in each orbital are found to obey a distinct set of Bethe-like equations. We construct the decay modes in the first orbital (containing the leading decay mode) in terms of an exact inhomogeneous matrix product ansatz, study the thermodynamic properties of the spectrum and the scaling of its gap, and provide a conjecture for the Bethe-like equations for all the orbitals and their degeneracy.

Ključne besede

markovske verige;integrabilnost;celični avtomati;Markov chains;integrability;reversible cellular automaton;nonequilibrium steady state;

Podatki

Jezik:	Angleški jezik
Leto izida:	2017
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
Založnik:	IOP Publishing Ltd
UDK:	519.217
COBISS:	3178340
ISSN:	1751-8113
Št. ogledov:	990
Št. prenosov:	621
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	markovske verige;integrabilnost;celični avtomati;
Konec prepovedi (OpenAIRE):	0000-00-00
Strani:	25 str.
Letnik:	ǂVol. ǂ50
Zvezek:	ǂart. no. ǂ395002
Čas izdaje:	2017
DOI:	10.1088/1751-8121/aa85a3
ID:	10915632