Models of hierarchically constrained dynamics for glassy relaxation

TLDR: In this paper, a class of models for relaxation in strongly interacting glassy materials is suggested, where degrees of freedom are divided into a sequence of levels such that those in level $n+1$ are locked except when some of those inlevel $n$ find the right combination to release them, representing the hierarchy of constraints in real systems.

Abstract: A class of models for relaxation in strongly interacting glassy materials is suggested. Degrees of freedom are divided into a sequence of levels such that those in level $n+1$ are locked except when some of those in level $n$ find the right combination to release them, this representing the hierarchy of constraints in real systems. The Kohlrausch anomalous relaxation law, $\mathrm{exp}[\ensuremath{-}{(\frac{t}{\ensuremath{\tau}})}^{\ensuremath{\beta}}]$, emerges naturally, and a maximum time scale is found which exhibits a Vogel-Fulcher-type temperature dependence.