The potential energy landscape and inherent dynamics of a hard-sphere fluid

TL;DR

This paper demonstrates that analyzing geodesic pathways in the potential energy landscape of hard-sphere fluids can predict their dynamic behavior, including diffusion decline and heterogeneity, without softening the potential.

Contribution

It introduces a method to calculate geodesic pathways in hard-sphere landscapes, linking landscape topology directly to dynamic properties without coarse-graining.

Findings

Geodesic pathway lengths grow rapidly with packing fraction.

Pathway lengths predict the decline in diffusion constants.

Landscape features forecast dynamic heterogeneity.

Abstract

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly non-analytic character of their potentials makes it a challenge to think of that behavior in potential-energy-landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential-energy landscape) correctly predict the occurrence of dynamic heterogeneity and non-zero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.