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In the kinetic theory of dense fluids the many-particle collision bracketintegral is given in terms of a classical collision operator defined in thephase space. To find an algorithm to compute the collision bracket integrals,we revisit the eigenvalue problem of the Liouville operator and re-examine themethod previously reported[Chem. Phys. 20, 93(1977)]. Then we apply the notionand concept of the eigenfunctions of the Liouville operator and knowledgeacquired in the study of the eigenfunctions to obtain alternative forms forcollision integrals. One of the alternative forms is given in the form of timecorrelation function. This form, on an additional approximation, assumes a formreminiscent of the Chapman-Enskog collision bracket integral for dilute gases.It indeed gives rise to the latter in the case of two particles. Thealternative forms obtained are more readily amenable to numerical simulationmethods than the collision bracket integras expressed in terms of a classicalcollision operator, which requires solution of classical Lippmann-Schwingerintegral equations. This way, the aforementioned kinetic theory of dense fluidsis made more accessible by numerical computation/simulation methods thanbefore.

Eigenfunctions for Liouville Operators, Classical Collision Operators, and Collision Bracket Integrals in Kinetic Theory