S. Sandow, PARTIALLY ASYMMETRIC EXCLUSION PROCESS WITH OPEN BOUNDARIES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(4), 1994, pp. 2660-2667
Exclusive diffusion on a one-dimensional lattice is studied. In the mo
del, particles hop stochastically in both directions but with differen
t rates. At the ends of the lattice, particles are injected and remove
d. The exact stationary probability measure is represented in the form
of a matrix product, as a generalization of the solution given by Der
rida et al. [J. Phys. A 26, 1493 (1993)] for the fully asymmetric proc
ess. The phase diagram of the current on the infinite lattice is obtai
ned. Analytic expressions for the current in the different phases are
derived. The model is equivalent to an XXZ-Heisenberg chain with a cer
tain type of boundary terms, the ground state of which corresponds to
the stationary solution of the master equation.