Spatial dimensionality dependence of long-time diffusion on two- and three-dimensional systems near glass transition

The long-time diffusion process of hard disks is compared with that of hard spheres by performing extensive event-driven molecular simulations. The volume fraction dependence of the mean-square displacements, the self-intermediate scattering function, and the non-Gaussian parameter of both systems are fully investigated. The singular function, which has been theoretically proposed for three-dimensional systems by Tokuyama [Physica, vol. 364 (2006) 23-62], is found to describe the long-time self-diffusion coefficient of both hard disks and hard spheres. The characteristic times of the β relaxation process and the α relaxation process of hard disks are also found to be similar to those of hard spheres when the particles had the same long-time self-diffusion coefficient. The spatial dimension d changes the value of the glass transition point and peak height of the non-Gaussian parameter which are related to the geometric packing characteristics of hard disks and hard spheres.