Vibrational Contribution to Density and Current Autocorrelations in a Monatomic Liquid

TL;DR

This paper analyzes the vibrational contributions to density and current autocorrelation functions in a monatomic liquid using the Vibration-Transit theory, proposing a practical computational approach to overcome multimode expansion challenges.

Contribution

It introduces a vibrational Hamiltonian framework within V-T theory for calculating autocorrelation functions and offers a direct numerical method to improve computational feasibility.

Findings

Vibrational contributions can be effectively isolated in autocorrelation functions.

Multimode expansion calculations are numerically challenging at high temperatures.

Direct computation and numerical Fourier transform provide a practical solution.

Abstract

We consider for a monatomic liquid the density and current autocorrelation functions from the point of view of the Vibration-Transit (V-T) theory of liquid dynamics. We also consider their Fourier transforms, one of which is measured by X-ray and neutron scattering. In this description, the motion of atoms in the liquid is divided into vibrations in a single characteristic potential valley, called a random valley, and nearly-instantaneous transitions called transits between valleys. The theory proposes a Hamiltonian for the vibrational motion, to be corrected to take transits into account; this Hamiltonian is used to calculate the autocorrelation functions, giving what we call their vibrational contributions. We discuss the multimode expansions of the autocorrelation functions, which provide a physically helpful picture of the decay of fluctuations in terms of n-mode scattering processes; we also note that the calculation and Fourier transform of the multimode series are numerically problematic, as successive terms require larger sums and carry higher powers of the temperature, which is a concern for the liquid whose temperature is bounded from below by melt. We suggest that these problems are avoided by directly computing the autocorrelation functions, for which we provide straightforward formulas, and Fourier transforming them numerically.