Glass transition and random walks on complex 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.

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• Spectral properties of the trap model on sparse networks
• Complex networks and glassy dynamics: walks in the energy landscape
• The Angell Plot from the Potential Energy Landscape Perspective
• Slow dynamics of Zero Range Process in the Framework of Traps Model