Configuration-tree theoretical calculation of the mean-squared displacement of particles in glass formers

We report an analytical evaluation of the mean-squared displacement (MSD) of the particles in glasses based on their coarse grained trajectories, after their vibrations are averaged out. The calculation is conducted by means of a local random configuration-tree theory that was recently proposed by one of us (Lam 2018 J. Stat. Mech. 023301). It assumes that system dynamics is dominated by activated particle hops initiated by voids and that particles are distinguishable with, in general, diverse properties. Results are compared with the numerical simulations of a lattice glass model, and satisfactory agreement has been obtained for various density of particles over a wide range of temperatures in the entire region of time with only two parameters.