Configuration-tree Theoretical Calculation of the Mean-Squared Displacement of Particles in Glass Formers

Abstract

We report an analytical evaluation of the mean-squared displacement (MSD) of the particles in glasses based on their coarse grained trajectories. The calculation is conducted by means of a local random configuration-tree theory that was recently proposed by one of us [C.-H. Lam, J. Stat. Mech. \textbf{2018}, 023301 (2018)]. Results are compared with the numerical simulations of a lattice glass model, and good quantitative agreement has been obtained over a wide range of temperatures in the entire region of time with virtually no free parameters. To the best of our knowledge, the calculation is the first in its kind.

arXiv comment11 pages, 2 figures

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• Diffusion coefficient power laws and defect-driven glassy dynamics in swap acceleration
• Emergence of two-level systems in glass formers: a kinetic Monte Carlo study
• Kovacs Effect in Glass with Material Memory Revealed in Non-Equilibrium Particle Interactions
• Large heat-capacity jump in cooling-heating of fragile glass from kinetic Monte Carlo simulations based on a two-state picture
• Surface mobility gradient and emergent facilitation in glassy films
• The distinguishable-particle lattice model of glasses in three dimensions