Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process

We consider current statistics for a two-species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step-type initial condition, we show that the limiting distribution is a product of the Gaussian and the Gaussian unitary ensemble Tracy-Widom distributions. This is the first analytic confirmation for a multicomponent system of a prediction from the recently proposed nonlinear fluctuating hydrodynamics for one-dimensional systems.