Measuring Many-Body Distribution Functions in Fluids using Test-Particle Insertion

TL;DR

This paper introduces a hierarchy of equations enabling the measurement of many-body distribution functions in fluids through test-particle insertion, improving structural resolution and normalization over traditional methods.

Contribution

The authors develop a novel insertion-based approach to measure n-body distribution functions, addressing limitations of conventional distance-histogram techniques.

Findings

Successfully measured pair and three-body distribution functions

Enhanced structural resolution compared to traditional methods

Applicable to inhomogeneous fluids and liquid state theory

Abstract

We derive a hierarchy of equations which allow a general $n$-body distribution function to be measured by test-particle insertion of between $1$ and $n$ particles, and successfully apply it to measure the pair and three-body distribution functions in a simple fluid. The insertion-based methods overcome the drawbacks of the conventional distance-histogram approach, offering enhanced structural resolution and a more straightforward normalisation. They will be especially useful in characterising the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory.