Abstract
It is known that a single product shock measure in some of the one-dimensional driven-diffusive systems with nearest-neighbor interactions might evolve in time quite similarly to a random walker moving on a one-dimensional lattice with reflecting boundaries. The nonequilibrium steady state of the system in this case can be written in terms of a linear superposition of such uncorrelated shocks. Equivalently, one can write the steady state of this system using a matrix-product approach with two-dimensional matrices. In this paper, we present an equilibrium two-dimensional one-transit walk model and find its partition function using a transfer matrix method. We will show that there is a direct connection between the partition functions of these two systems. We will explicitly show that in the steady state, the transfer matrix of the one-transit walk model is related to the matrix representation of the algebra of the driven-diffusive model through a similarity transformation. The physical quantities are also related through the same transformation.
- Received 25 October 2009
DOI:https://doi.org/10.1103/PhysRevE.81.011119
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