Factorization of 3-point static structure functions in 3D Yukawa liquids

TL;DR

This study examines the validity of the convolution approximation for 3-point static structure functions in 3D Yukawa liquids, revealing its breakdown at high coupling and the emergence of negative values indicating sign changes in density response.

Contribution

The paper provides the first detailed molecular dynamics analysis of the factorization approximation in strongly-coupled Yukawa liquids, highlighting its limitations at high coupling.

Findings

Factorization breaks down at high coupling.

Negative values of $S^{(3)}$ appear at strong coupling.

Sign change in the quadratic density response observed.

Abstract

In many-body systems the convolution approximation states that the 3-point static structure function, $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, can approximately be "factorized" in terms of the 2-point counterpart, $S^{(2)}(\textbf{k}_{1})$. We investigate the validity of this approximation in 3-dimensional strongly-coupled Yukawa liquids: the factorization is tested for specific arrangements of the wave vectors $\textbf{k}_{1}$ and $\textbf{k}_{2}$, with molecular dynamics simulations. With the increase of the coupling parameter we find a breakdown of factorization, of which a notable example is the appearance of negative values of $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, whereas the approximate factorized form is restricted to positive values. These negative values -- based on the quadratic Fluctuation-Dissipation Theorem -- imply that the quadratic part of the density response of the system changes sign with wave number. Our simulations that incorporate an external potential energy perturbation clearly confirm this behavior.