Dynamical arrest, tracer diffusion and Kinetically Constrained Lattice Gases

TL;DR

This paper investigates particle diffusion in kinetically constrained lattice models for glasses, establishing bounds and exact density dependence of the self diffusion coefficient, and challenging the existence of a finite-temperature dynamical transition.

Contribution

It introduces a method to derive bounds and exact density dependence of diffusion in kinetically constrained models, including the Kob-Andersen model, and rules out finite-temperature dynamical transitions.

Findings

Derived bounds for the self diffusion coefficient D_S.

Established the exact density dependence of D_S at high density.

Proved the absence of a finite-temperature dynamical transition in these models.

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 particles on a lattice.