Exclusion processes with avalanches

Variational calculation of transport coefficients in diffusive lattice gases

A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient can be computed only in the exceptional situation when the lattice gas is gradient. In the general case, minimization over an infinite-dimensional space is required. We propose an approximation scheme based on minimizing over finite-dimensional subspaces of functions. The procedure is demonstrated for one-dimensional generalized exclusion processes in which each site can accommodate at most two particles. Our analytical predictions provide upper bounds for the diffusivity that are very close to simulation results throughout the entire density range. We also analyze nonequilibrium density profiles for finite chains coupled to reservoirs. The predictions for the profiles are in excellent agreement with simulations.

Generalized exclusion processes: Transport coefficients

A class of generalized exclusion processes with symmetric nearest-neighbor hopping which are parametrized by the maximal occupancy, k≥1, is investigated. For these processes on hypercubic lattices we compute the diffusion coefficient in all spatial dimensions. In the extreme cases of k=1 (symmetric simple exclusion process) and k=∞ (noninteracting symmetric random walks) the diffusion coefficient is constant, while for 2≤k<∞ it depends on the density and k. We also study the evolution of the tagged particle, show that it exhibits a normal diffusive behavior in all dimensions, and probe numerically the coefficient of self-diffusion.