Kinetic Theory of a Dense Gas: Properties of Collision Kernels of the Bogoliubov Type

Abstract

We study the collision kernels of two linearized equations for a moderately dense gas. These are the low-density Bogoliubov kinetic equation and the equation at the next order in the density (ternary-collision level), in the form given by Green and Cohen. We reduce the collision kernels of these equations to expressions which are nonlocal in space but local in time, and show that each of them breaks up into static and collisional parts. The former parts agree with the mean-field expressions. We compare the collisional parts with the fully dynamical expressions previously found by Mazenko and us, and find complete agreement only at zero wave vector and frequency. For nonzero wave vectors, the desired symmetry in the momentum variables breaks down. We show that this has no effect on the first-order transport coefficients; it would presumably be significant in the kinetic regime. We also find that the speed of sound predicted by the Bogoliubov equation agrees with the thermodynamic result truncated at first order in the density.