Exact matrix product decay modes of a boundary driven cellular automaton

Prosen, Tomaž (avtor), Buča, Berislav (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Markov chains, integrability, reversible cellular automaton, nonequilibrium steady state
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Založnik: IOP Publishing Ltd
• Leto izida: 2017
• Št. strani: 25 str.
• Številčenje: Vol. 50, art. no. 395002
• PID: 20.500.12556/RUL-100073
• UDK: 519.217
• ISSN pri članku: 1751-8113
• DOI: 10.1088/1751-8121/aa85a3
• COBISS.SI-ID: 3178340
• Datum objave v RUL: 02.03.2018

Gradivo je del revije

• Naslov: Journal of physics : Mathematical and theoretical
• Skrajšan naslov: J. phys., A, Math. theor.
• Založnik: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
• Začetek licenciranja: 02.03.2018

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: markovske verige, integrabilnost, celični avtomati

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open many-body non-equilibrium systems
• Akronim: OMNES