Hopping times of two hard disks diffusing in a channel

A finite difference method was used to solve numerically the multidimensional diffusion equation describing the time evolution of two hard disks diffusing in a narrow hard channel. The authors extract an estimate for the average time tauhop needed for the disks to hop pass each other. For narrow channels near the hopping threshold, tauhop diverges and is consistent with the scaling prediction of the transition state theory. This provides a much-needed rigorous benchmark to test an approximate solution to the diffusion problem.