On the ubiquity of matrix-product states in one-dimensional stochastic processes with boundary interactions

Kai Klauck and Andreas Schadschneider

Physica A: Statistical Mechanics and its Applications, 1999, vol. 271, issue 1, 102-117

Abstract: Recently, it has been shown that the zero-energy eigenstate – corresponding to the stationary state – of a stochastic Hamiltonian with nearest-neighbour interaction in the bulk and single-site boundary terms, can generically be written in the form of a so-called matrix-product state. We generalize this result to stochastic Hamiltonians with arbitrary, but finite, interaction range. As an application two different particle-hopping models with three-site bulk interaction are studied. For these models which can be interpreted as cellular automata for traffic flow, we present exact solutions for periodic boundary conditions and some suitably chosen boundary interactions.

Keywords: Stochastic many-body systems; Reaction-diffusion models; Nonequilibrium stationary state; Traffic-flow (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:271:y:1999:i:1:p:102-117

DOI: 10.1016/S0378-4371(99)00176-4

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