Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open   Boundaries
  We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes. 
Jan de Gier and Fabian H.L. Essler