Transition state theory and the dynamics of hard disks

TL;DR

This paper compares molecular dynamics simulations of confined hard disks with transition state theory predictions, extending the theory to many disks and relating it to glassy dynamics in three dimensions.

Contribution

It generalizes transition state theory to many hard disks and validates it against simulations, connecting microscopic dynamics to macroscopic relaxation.

Findings

Transition state theory accurately predicts disk dynamics in confined systems.

Generalization of the theory to many disks matches simulation results.

Derivation of Vogel-Fulcher-Tammann formula for 3D hard spheres.

Abstract

The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.