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.
2017
2018-03-02 14:51:25
1033
Markov chains, integrability, reversible cellular automaton, nonequilibrium steady state
markovske verige, integrabilnost, celični avtomati
IOP Publishing Ltd
Tomaž
Prosen
70
Berislav
Buča
70
UDK
4
519.217
ISSN pri članku
9
1751-8113
DOI
15
10.1088/1751-8121/aa85a3
COBISS_ID
3
3178340
OceCobissID
13
3692314
RAZ_Prosen_Tomaz_2017.pdf
1692357
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2018-03-05 08:33:20