Failure of Bogoliubov's Functional Assumption

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Abstract
In this paper we investigate the mathematical validity of Bogoliubov's functional assumption. For this purpose, we analyze a model for a system in which light particles scatter against fixed centers. We compare the exact solution for the one-body distribution function and two-body correlation function with the results given by Bogoliubov's method. We find that Bogoliubov's functional assumption is too restrictive to allow proper initialization for both functions. As a consequence, the Bogoliubov result for the two-body correlation departs drastically from the exact solution. The results obtained here are fully consistent with previous asymptotic analysis of the one- and two-body equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarcy.