Long time expansion of two-dimensional correlation functions

We show that the long time behaviour of the velocity correlation function in a two-dimensional classical system with pairwise repulsive potentials can be represented by a series expansion of the form 〈υ1xυ1x(t)〉 = d0t−1 + d1t−1log t/t0 + d2t−1(log t/t0)2 + …, where t0 is mean free time between collisions. To lowest order in the density an exact expression has been obtained for d1 employing the kinetic theory ofsystems with hard-core interactions. The significance of the series is discussed at low and intermediate densities.