Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane

TL;DR

This study uses Molecular Dynamics simulations to investigate how negative curvature in the hyperbolic plane influences particle dynamics in a monatomic Lennard-Jones liquid, leading to glass formation and characteristic slow dynamics.

Contribution

It demonstrates that negative curvature frustrates crystallization, resulting in glassy behavior and slow dynamics similar to real glassformers, within a hyperbolic geometry model.

Findings

Emergence of a plateau in mean square displacement at intermediate times

Decoupling of local relaxation time and diffusion constant

Avoidance of crystallization due to geometric frustration

Abstract

We study by Molecular Dynamics simulation the slowing down of particle motion in a two-dimensional monatomic model: a Lennard-Jones liquid on the hyperbolic plane. The negative curvature of the embedding space frustrates the long-range extension of the local hexagonal order. As a result, the liquid avoids crystallization and forms a glass. We show that, as temperature decreases, the single particle motion displays the canonical features seen in real glassforming liquids: the emergence of a "plateau" at intermediate times in the mean square displacement and a decoupling between the local relaxation time and the (hyperbolic) diffusion constant.