  The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional
periodic substrate with varied widths is investigated using Langevin dynamical
simulations. When the substrate is narrow and the dust particles form a single
row, the diffusion is the smallest in both directions. We find that as the
substrate width gradually increases to twice its initial value, the long-time
diffusion of the two-dimensional dusty plasmas first increases, then decreases,
and finally increases again, giving an oscillation-like diffusion with varied
substrate width. When the width increases to a specific value, the dust
particles within each potential well arrange themselves in a stable zigzag
pattern, greatly reducing the diffusion, and leading to the observed
oscillation in the diffusion with the increasing width. In addition, the
long-time oscillation-like diffusion is consistent with the number of dust
particles that are hopping across the potential wells of the substrate.
