On the Calculation of Autocorrelation Functions of Dynamical Variables

Abstract

In this paper we develop a formalism for calculating the autocorrelation function of a dynamical variable in terms of a well-defined memory function. Guided by simple physical arguments, an ansatz is adopted for the functional form of the memory function. This ansatz asserts that the memory of dynamical coherence decays exponentially. It is found that: (a) Despite the monotonic exponential decay of the memory function, the autocorrelation function deduced can display negative regions in some circumstances and decay monotonically in other circumstances. (b) The form of the autocorrelation function deduced is identical with that obtained from two other very different analyses, suggesting that the major properties of the function are of general validity. (c) The computed linear momentum autocorrelation function and power spectrum for liquid Ar are in good agreement with the computer experiments of Rahman. (d) The computed dipolar autocorrelation function reproduces all the features of the experimentally determined autocorrelation function, though at present insufficient data are available to provide a quantitative test of the theory. (e) The ansatz used, although obviously not exact, is consistent with the theory of linear regression (Appendix B).