Long time behaviour of four point velocity correlations in hard disk systems

An asymptotic long time expansion is derived for the time dependent super Burnett coefficient which is the time derivative of the fourth cumulant of displacement of a tagged particle in a hard disk system or, alternatively, it is the ordered time integral over the cumulant of the four point velocity correlation function. Use has been made of a kinetic theory for hard disk systems. In contrast to classical theories the super Burnett coefficient shows a rather strong divergence, proportional to t. The theoretical prediction is compared with results from molecular dynamics