Diffusion of noninteracting particles into a semi-infinite lattice

Consider a gas of noninteracting particles diffusing into a semi-infinite lattice, Z+×ZD−1, subject to exclusion of double occupancy. An exact closed set of equations can be obtained and solved (in closed form) for the single-site occupancies or densities. Equations for the n-site occupancies couple only to such functions for n and n-1 sites, as for an infinite lattice. Their analysis reveals that negative pair correlations develop during this process, reflecting the propensity for diffusion to reduce density inhomogeneities and fluctuations