20.500.12556/RUL-100073 Exact matrix product decay modes of a boundary driven cellular automaton 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. Markov chains integrability reversible cellular automaton nonequilibrium steady state markovske verige integrabilnost celični avtomati true false false IOP Publishing Ltd Angleški jezik Slovenski jezik Neznano 2018-03-02 14:51:25 2018-03-02 14:51:25 2022-08-24 17:15:33 0000-00-00 00:00:00 2017 0 0 25 str. art. no. 395002 Vol. 50 2017 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0000-00-00 519.217 1751-8113 10.1088/1751-8121/aa85a3 3178340 3692314 RAZ_Prosen_Tomaz_2017.pdf RAZ_Prosen_Tomaz_2017.pdf 1 1C54DFCD39BEA9B7BC08247790906639 dd454aae185e530dbaf44508acd944ad07743a324d022a7d52aa4d6c5a5f5acc b8a03217-a1bb-11eb-a523-00155dcfd717 20.500.12556/rul/f24f48d7-1016-4769-901f-aa30d7a3ade9 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=141232 http://iopscience.iop.org/article/10.1088/1751-8121/aa85a3 1 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=109746 Fakulteta za matematiko in fiziko 0 0 0