Replica theory for fluctuations of the activation barriers in glassy systems

TL;DR

This paper develops a theoretical framework to understand the fluctuations of activation barriers in glassy systems, linking configurational entropy, surface tension, and dynamic heterogeneity, and highlights the Gaussian nature of barrier distributions.

Contribution

It introduces an effective potential approach to quantify barrier fluctuations and relates them to dynamic heterogeneity in glassy systems, emphasizing the role of entropy and surface tension fluctuations.

Findings

Barrier fluctuations are crucial for understanding heterogeneous dynamics.

Diluted entropic droplets exhibit Gaussian barrier distributions.

A relation between dynamic heterogeneity length scale and barrier fluctuations is derived.

Abstract

We consider the problem of slow activation dynamics in glassy systems undergoing a random first order phase transition. Using an effective potential approach to supercooled liquids, we determine the spectrum of activation barriers for entropic droplets. We demonstrate that fluctuations of the configurational entropy and of the liquid glass surface tension are crucial to achieve an understanding of the barrier fluctuations in glassy systems and thus are ultimatively responsible for the broad spectrum of excitations and heterogeneous dynamics in glasses. In particular we derive a relation between the length scale for dynamic heterogeneity and the related barrier fluctuations. Diluted entropic droplets are shown to have a Gaussian distribution of barriers, strongly suggesting that non-Gaussian behavior results from droplet-droplet interactions.