A new microscopic evaluation method for correlation functions: Long time tails

Considering a moderately dense fluid, whose N particles interact with a general short-range repulsive potential, we show that the momentum autocorrelation function (associated with self-diffusion processes) has a long time tail of the form t ^{-d 2} (d = 2, 3: number of dimensions). Thereby new powerful concepts, in particular the P_q-rule and the P_q-singularity (the latter being a generalization of van Hove's diagonal singularity) are introduced in order to select the most divergent terms of the density expansion of the correlation function in the thermodynamic and long time limit. It turns out that this method is more suitable for removing a special class of divergences than the Zwanzig inversion method applied by previous workers in this field.