Partially Asymmetric Exclusion Process with Open Boundaries

Details Partially Asymmetric Exclusion Process with Open Boundaries Partially Asymmetric Exclusion Process with Open Boundaries

1994-05-25

arxiv.org/abs/cond-mat/9405073v1

Physics

Condensed Matter

11 pages RevTex, one figure as postscriptfile appended which should be saved as "phases.ps"

Scientific paper

10.1103/PhysRevE.50.2660

Exclusive diffusion on a one-dimensional lattice is studied. In the model particles hop stochastically into both directions with different rates. At the ends of the lattice particles are injected and removed. The exact stationary probability measure is represented in form of a matrix product as a generalization of the solution given by Derrida et al \cite{dehp} for the fully asymmetric process. The phase diagram of the current on the infinite lattice is obtained. Analytic expressions for the current in the different phases are derived. The model is equivalent to a $XXZ$-Heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation.

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