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 particles on a lattice.

28 pages, 4 figures

References in corpus (3)

• Glassy dynamics of kinetically constrained models
• Lattice Glass Models
• Spatial structures and dynamics of kinetically constrained models for glasses

Cited by in corpus (11)

• Heterogeneity and growing lengthscales in the dynamics of kinetically constrained lattice gases in two dimensions
• Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
• Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Bulk diffusion in a kinetically constrained lattice gas
• Bootstrap percolation and kinetically constrained models on hyperbolic lattices
• Jamming percolation and glassy dynamics
• Spiral model, jamming percolation and glass-jamming transitions
• Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet
• Dynamic propensity in a kinetically constrained lattice gas
• Dynamic facilitation explains democratic particle motion of metabasin transitions