Models of Hierarchically Constrained Dynamics for Glassy Relaxation

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 $n+1\mathrm{}$ 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, $\exp [-{\left(\frac{t}{\tau }\right)}^{\beta }]$, emerges naturally, and a maximum time scale is found which exhibits a Vogel-Fulcher-type temperature dependence.