Normal versus anomalous self-diffusion in two-dimensional fluids: Memory   function approach and generalized asymptotic Einstein relation
  Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities. 
Hyun Kyung Shin, Bongsik Choi, Peter Talkner, Eok Kyun Lee
cond-mat.soft cond-mat.stat-mech