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

Abstract

In many-body systems the convolution approximation states that the 3-point static structure function, $S^{(3)}({\text{k}}_1,{\text{k}}_2)$, can approximately be "factorized" in terms of the 2-point counterpart, $S^{(2)}({\text{k}}_1)$. 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 ${\text{k}}_1$ and ${\text{k}}_2$, 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 $S^{(3)}({\text{k}}_1,{\text{k}}_2)$, 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.