Kinetic theory of rough sphere fluids: Linear and angular velocity correlation functions

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Abstract
We present a renormalized kinetic theory for tagged particle motion in a rough sphere fluid which includes the effects of correlated collisions. The kinetic theory is a generalization of a recent theory for monatomic fluids by Mazenko. The correlated collisions create slowly decaying memory in the linear (ψv) and angular (ψω) velocity correlation functions on account of the coupling of the test particle density fluctuations to various moments of the full phase space density correlation function. (These moments are connected with the conserved variables in the system). We use the theory to study ψv and ψω and compare the results with recent molecular dynamics experiments of O’Dell and Berne. The kinetic theory yields the correct long time power law decay for both ψv and ψω without imposing any wave vector cutoff characteristic of the hydrodynamic theories. It also yields useful new insights into various mode couplings responsible for the behavior of ψv and ψω at small and intermediate times. The qualitative features of the computer experiments are reproduced by the theory.