Glass transition and random walks on complex energy landscapes

TL;DR

This paper introduces a mathematical model of glassy dynamics using random walks on directed, weighted networks representing energy landscapes, emphasizing the importance of network topology and energy-minima relationships.

Contribution

It provides a novel framework applying complex network theory to analyze energy landscapes and glassy dynamics, extending beyond small system studies.

Findings

Highlights the role of network topology in glassy dynamics

Connects energy minima properties with network structure

Proposes a generalized approach for studying energy landscapes

Abstract

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the energies of the minima and their number of neighbors should be studied in connection with the network's global topology, and show how the tools developed in complex network theory can be put to use in this context.