Self-diffusion coefficient in the Kob-Andersen model

Abstract

The Kob-Andersen model is a fundamental example of a kinetically constrained lattice gas, that is, an interacting particle system with Kawasaki type dynamics and kinetic constraints. In this model, a particle is allowed to jump when sufficiently many neighboring sites are empty. We study the motion of a single tagged particle and in particular its convergence to a Brownian motion. Previous results showed that the path of this particle indeed converges in diffusive time-scale, and the purpose of this paper is to study the rate of decay of the self-diffusion coefficient for large densities. We find upper and lower bounds matching to leading behavior.