Perturbative Theory of Self-Diffusion in Classical Many-Particle Systems. I. Velocity Autocorrelation Function

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Abstract
To investigate the diffusive motion of a test particle in a classical many-body system, the projection-operator formalism of Zwanzig has been applied to the calculation of the velocity autocorrelation function. The memory kernel in this formalism is investigated by using a perturbation expansion in a parameter characteristic of the time scale of correlations in the system. General studies of the asymptotic time behavior of the correlation function are given, as well as several explicit calculations for modeled interparticle potentials.