Exact results for one-dimensional totally asymmetric diffusion models

Abstract

Several types of totally asymmetric diffusion models with and without exclusion are considered. For some models, conditional probabilities of finding N particles on lattice sites at time t with initial occupation at time t = 0 are expressed in a determinant form. On the other hand, the q-boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion-like interaction. The effects of the interaction are compared for the case of two-particle diffusion.