Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries

Abstract

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, a method introduced recently to study the spin chain with non-diagonal boundaries. We provide in this case a proof of this method.