Spectrum of the Open Asymmetric Simple Exclusion Process with Arbitrary Boundary Parameters**Supported by the National Natural Science Foundation of China under Grant Nos 11375141, 11475135, 11434013 and 11425522, the Ministry of Education Doctoral Program Fund under Grant No 20126101110004, and the Northwest University Graduate Student Innovation Fund under Grant No YZZ14104.

Abstract

We study the one-dimensional asymmetric simple exclusion process (ASEP) with generic open boundaries (including current-counting deformation), and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.