Memory Function for the Autoregressed Velocity Autocorrelation Function of a Dense Liquid

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Abstract
The analytical form of the memory function K(t) is derived by using the resolved modes of the autoregressed velocity autocorrelation function. By this analysis a new representation for K(t) of a dense soft-core liquid is obtained in a form of a linear combination of one damped exponential and more than two damped cosines. The characteristic features of K(t) which have been indicated by molecular dynamics simulations for dense classical liquids can be interpreted clearly by the use of each component appearing in our K(t), i.e., steep initial decay, subsequent redevelopment at intermediate times, and very slow final decay. The results are discussed with the aid of Gaussian and exponential memories.

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