Generalized Bethe ansatz solution of one-dimensional asymmetric exclusion process on a ring with blockage

We present and solve for an one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring with a single defect, across which particlesmove with probability 0≤p≥1. This model is equivalent to a two-dimensional six-vertex model in an extreme anisotropic limit with defect line interpolating between open boundary conditions and periodic translationally invariant boundary conditions. We give a solution using Bethe ansatz methods generelized to this kind of boundary conditions. In particular we discuss the steady state and give an exact expression of average occupation number of particles as a function of the position on the lattice. In the limit of infinite length L the phase diagram turns out to be qualitatively the same as for the probabilistic asymmetric exclusion process on the ring with a defect. The density profile for L large but finite is computed in the different phases. In the coexistence phase the width δ of the interface between the high density region and the low density region is shown to grow as L1/2 with the length of the system if the density ρ is not close to the 1/2 and to be 0 independent of the size of the ring if ρ=1/2. (author)