Time and length scales for diffusion in liquids

The first six even moments of the displacement of a molecule in water and an atom in liquid argon are found by molecular dynamics simulations and compared with the moments predicted by diffusion theory. We find a noticeable difference between the moments higher than the second. The ratio between predicted and calculated moments approaches unity as $1/t$ for times larger than 10 ps. Continuous time random walk is used to explain this slow approach of the moments to their diffusion limit.