A toy model for viscous liquid dynamics

TL;DR

This paper introduces a high-dimensional geometric model that effectively simulates viscous liquid dynamics, capturing key features like slowing down and displacement behavior observed in real liquids.

Contribution

The paper presents a novel high-dimensional geometric toy model that mimics viscous liquid dynamics and aligns with established simulation results.

Findings

Model exhibits viscous dynamics above percolation threshold in multiple dimensions

Mean-squared displacement shows significant slowing down similar to real liquids

Shape of displacement closely matches that of Kob-Andersen binary Lennard Jones mixture

Abstract

A simple model for viscous liquid dynamics is introduced. Consider the surface of the union of hyper-spheres centered at random positions inside a hypercube with periodic boundary conditions. It is argued and demonstrated by numerical simulations that at high dimensions geodetic flows on this surface is a good model for viscous liquid dynamics. It is shown that this simple model exhibits viscous dynamics for densities above the percolation threshold in $8$, $12$ and $16$ dimensions. Thus the slowing down of the dynamics, measured by the mean-squared displacement, extends to several orders of magnitude similarly to what is observed in other models for viscous dynamics. Furthermore, the shape of the mean-squared displacement is to a very good approximation the same as for the standard model in simulations of viscous liquids: the Kob-Andersen binary Lennard Jones mixture.