Generalized Exclusion Processes: Transport Coefficients

A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.