Tomaž Prosen (Author), Berislav Buča (Author)

Abstract

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.

Keywords

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

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: IOP Publishing Ltd
UDC: 519.217
COBISS: 3178340 Link will open in a new window
ISSN: 1751-8113
Views: 990
Downloads: 621
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Other data

Secondary language: Slovenian
Secondary keywords: markovske verige;integrabilnost;celični avtomati;
Embargo end date (OpenAIRE): 0000-00-00
Pages: 25 str.
Volume: ǂVol. ǂ50
Issue: ǂart. no. ǂ395002
Chronology: 2017
DOI: 10.1088/1751-8121/aa85a3
ID: 10915632