On the stationary BBGKY hierarchy for equilibrium states

FM 4-12, arxiv:1205.2788

Authors G. Genovese, S. Simonella

Abstract: We establish a new direct integration method to construct the solutions of the stationary BBGKY hierarchy, assuming the usual Gaussian distribution of momenta. We prove equivalence between the corresponding infinite hierarchy and the Kirkwood and Salsburg equations. A problem of existence and uniqueness of the solutions of the hierarchy with appropriate boundary conditions is thus solved for low densities. The result is extended in a milder sense to systems with a hard core interaction.