Algebraic Bethe ansatz for the totally asymmetric simple exclusion   process with boundaries
  We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using the modified algebraic Bethe ansatz, method introduced recently to study the spin chain with non-diagonal boundaries. We provide in this case a proof of this method. 
Nicolas Crampe
math-ph cond-mat.stat-mech math.MP nlin.SI