On the Stationary BBGKY Hierarchy for Equilibrium States

摘要

We consider infinite classical systems of particles interacting via a smooth, stable and regular two-body potential. 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-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.