This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the $n$-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

This paper studies the single-file diffusion process on a linear chain of identical pointlike particles with multiple-site occupation confined in a one-dimensional box. The particles are noninteracting, except that double occupancy is forbidden. When particles are confined in a finite box, the final stage is saturation. By means of combinatorial analysis, an exact numerical evaluation of the saturation values for both the mean-square displacement (MSD) of a tracer particle and the center of mass of the system are obtained. Different initial distributions of particles are introduced. The time dependence of the MSD is obtained by means of Monte Carlo simulations. The values of the MSD for the tracer particles as well as the center of mass of the system depend on the size of the particle, the size of the box, and the initial distribution. Moreover, the transient regime depends on the initial distribution. In fact, the crossover from normal to subdiffusive regime is observed for random and alternate initial distributions, while superdiffusive diffusion appears for any stacked initial distributions. In all cases, it is shown that the collisions between particles do not determine the time exponent of the MSD. A simple expression for the transient regime is also obtained for the especial case of random initial distribution.

The exact expression for the collective diffusion coefficient in one dimension, obtained by Payne and Kreuzer [Phys. Rev. B. 75, 115403 (2007)], is compared with Monte Carlo simulation. Different hopping kinetics are analyzed. For initial-and final-state interaction kinetics no anomalies are observed. However, for the so-called interaction kinetics where both initial-and final-state interactions are involved, it is shown that even when the transition rates satisfy the principle of detail balance, additional constraints are necessary to guarantee the diffusion of particles. These restrictions give rise to a phase diagram that determines the regions where the exact solution of the diffusion coefficient seem to be not physically sound. The Monte Carlo simulation allows us to analyze the mechanism of diffusion in these regions, where in some cases the simulation does not match the exact solution. A possible explanation is presented.