  We report results of molecular dynamics simulations of a binary Lennard-Jones
system at zero pressure in the undercooled liquid and glassy states. We first
follow the evolution of diffusivity and dynamic heterogeneity with temperature
and show their correlation. In a second step we follow the ageing of a quenched
glass. As diffusivity decreases with ageing, heterogeneity increases. We
conclude that the heterogeneity is a property of the inherent diffusion of the
relaxed state. The variations with aging time can be explained by annealing of
quenched defect structures. This annealing has the same decay constants for
both diffusivity and heterogeneity of both components. \
