  We study an exclusion process on a ring comprising a free defect particle in
a bath of normal particles. The model is one of the few integrable cases in
which the bath particles are partially asymmetric. The presence of the free
defect creates localized or shock phases according to parameter values. We use
a functional approach to Bethe equations resulting from a nested Bethe ansatz
to calculate exactly the mean currents and diffusion constants. The results
agree very well with Monte-Carlo simulations and reveal the main modes of
fluctuation in the different phases of the steady state.
