An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state is known for all system sizes less thanN, then our equation (8) gives the steady state for sizeN. Using this recursion, we obtain closed expressions (48) for the average occupations of all sites. The results are compared to the predictions of a mean field theory. In particular, for infinitely large systems, the effect of the boundary decays as the distance to the power –1/2 instead of the inverse of the distance, as predicted by the mean field theory.