Activated Dynamics and the Ergodic-Nonergodic Transition

TL;DR

This paper introduces a hindered diffusion model for conserved density dynamics, revealing an ergodic-nonergodic transition with activated kinetics at low temperatures and high densities, compatible with mode-coupling theory.

Contribution

It presents a new continuum model that captures activated dynamics and the ergodic-nonergodic transition, extending understanding of glassy behavior in constrained systems.

Findings

Model exhibits an ergodic-nonergodic transition.

Supports activated kinetics in the nonergodic phase.

Compatible with mode-coupling theory.

Abstract

The hindered diffusion model is introduced. It is a continuum model giving the dynamics of a conserved density. Similar to the spin-facilitated models, the kinetics are hindered by a fluctuating diffusion coefficient that decreases as the local density approaches some geometrically constrained value where the mobility goes to zero. The model leads in a natural way to activated dynamics at low temperatures and high densities. In a well defined approximation the theory is shown to be compatible with mode-coupling theory. Indeed in the simplest form of the model we find an ergodic-nonergodic transition into a phase that supports activated kinetics and nonergodic behavior.