F H Jafarpour and S R Masharian J. Stat. Mech. (2007) P10013 doi:10.1088/1742-5468/2007/10/P10013
F H Jafarpour1,3 and S R Masharian2
Show affiliationsIt is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These solutions describe the diffusive motion of a product shock or a domain wall with the dynamics of a simple biased random walker. The steady state of these systems can be written in terms of linear superposition of such shocks or domain walls. These steady states can also be expressed in a matrix product form. We show that, in this case, the associated quadratic algebra of the system always has a two-dimensional representation with a generic structure. A couple of examples for the n = 1 and 2 cases are presented.
E-print Number: 0707.4341
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Refers: to
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
Issue 10 (October 2007)
Received 1 August 2007, accepted for publication 7 October 2007
Published 24 October 2007
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