Self-diffusion in a monatomic glass-forming liquid embedded in the hyperbolic plane

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 glass-forming 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.

Keywords:

• geometric frustration
• diffusion
• geometry
• glass transition