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

## TL;DR

This paper presents the first analytical calculation of the mean-squared displacement in glass formers using a configuration-tree theory, showing excellent agreement with simulations across various temperatures.

## Contribution

It introduces a novel analytical approach based on a local random configuration-tree theory to evaluate particle MSD in glasses, validated by numerical simulations.

## Key findings

- Good quantitative agreement with simulations across temperatures
- First analytical calculation of MSD in glasses using this method
- No free parameters used in the model

## 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.