Diffusion of particles interacting via long-range and oscillating forces in one dimension

Collective diffusion coefficient in a one-dimensional lattice gas adsorbate is calculated using variational approach. Particles interact via either a long-range, or a long-range electron-gas-mediated (for a metallic substrate), or a 12-6 Lennard-Jones interaction. Diffusion coefficient as a function of the adsorbate density strongly depends on the relationship between the substrate lattice constant and the characteristic length of the interparticle interaction potential (which determines positions of the potential energy minima). The diffusion coefficient at fixed density as a function of the interaction characteristic length has an oscillating character due to the interplay between the interparticle distances allowed by the substrate lattice structure and the average interparticle distances which minimize the total interaction energy.