Exact Stationary States of a Two-Dimensional Transport Model

Previous calculations of transport coefficients of particle systems in two or more dimensions have used computer simulations or various approximations, like those implicit in the Boltzmann equation or in the standard probability theory of diffusion. Here an exactly solved model of crystal growth in three dimensions is transformed into a 2D model of steady particle transport. Then the exact, many-body stationary distribution and exact transport coefficients can be found as well as correlation functions. The model is highly asymmetric. In the transverse direction, particles are strongly attracted, so that long transverse rows of particles tend to form at low temperature. Kinks in these rows are rare, so the transverse positions of kinks effectively move continuously on a large distance scale.