Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape

TL;DR

This paper demonstrates that the geometry of the potential energy landscape, specifically geodesic path lengths, directly correlates with the slow dynamics and glass transition behavior in liquids and supercooled systems.

Contribution

It introduces the potential energy landscape ensemble framework, linking geodesic path lengths to system dynamics and providing a numerical method to analyze these paths.

Findings

Geodesic lengths increase as systems approach glass transition.

The temperature dependence of diffusion constants is predicted by geodesic growth.

Geodesic analysis accurately captures the dynamics of atomic liquids and glasses.

Abstract

How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential energy landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics - the shortest paths through their landscapes within the special ensemble. The more convoluted and labyrinthine these geodesics are, the slower that dynamics is. Geodesics in the landscape ensemble have sufficiently well-defined characteristics that is straightforward to search for them numerically, a point we illustrate by computing the geodesic lengths for an ordinary atomic liquid and a binary glass-forming atomic mixture. We find that the temperature dependence of the diffusion constants of these systems, including the precipitous drop as the glass-forming system approaches its mode-coupling transition, is predicted quantitatively by the growth of the geodesic path lengths.