Memory Effects and the Autocorrelation Function of a Dynamical Variable

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Abstract
In this paper we apply the theory of irreversible processes, as developed by Prigogine and co-workers, to derive the transport equation describing the time evolution of the autocorrelation function of a phase function. We show that the memory function which enters the master equation derived by Nakajima and Zwanzig (NZ) can be formally expressed in terms of the collision operator and the destruction operator which appear in the master equation of Prigogine and Resibois (PR). Because the forms of the collision and destruction operators are complex and not known in explicit terms, a simple model is used to compute the momentum autocorrelation function for a strongly coupled system. Despite the simplifications introduced by the model, amongst which is the use of an exponential repulsion between pairs of atoms, some comparison of theory and observation is valuable. Accordingly, we have made a comparison between our theoretical results and Rahman's ``experimental'' data for liquid argon. The time dependence of the destruction term is also discussed and explicitly calculated for a particular model.