Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

We analyse the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained recently for totally asymmetric diffusion (de Gier J and Essler F H L 2006 J. Stat. Mech. P12011) to the case of partial asymmetry. We determine the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at late times, in the low- and high-density regimes and on the coexistence line. We observe boundary-induced crossovers and discuss possible interpretations of our results in terms of effective domain wall theories