Dynamical Arrest, Tracer Diffusion and Kinetically Constrained Lattice Gases

Abstract

We analyze the tagged particle diffusion for kinetically constrained models for glassy systems. We present a method, focusing on the Kob–Andersen model as an example, which allows to prove lower and upper bounds for the self-diffusion coefficient D _S. This method leads to the exact density dependence of D _S, at high density, for models with finite defects and to prove diffusivity, D _S > 0, at any finite density for highly cooperative models. A more general outcome is that under very general assumptions one can exclude that a dynamical transition, like the one predicted by the Mode-Coupling-Theory of glasses, takes place at a finite temperature/chemical potential for systems of interacting particle on a lattice.