Density Renormalization Group for Classical Liquids

TL;DR

This paper introduces density renormalization group equations (DRGEs) that describe how liquid correlation functions change with density, enabling the calculation of high-density liquid properties from lower-density data.

Contribution

It develops a new set of differential equations, DRGEs, for liquid correlation functions, extending the BBGKY hierarchy through Legendre transformations for improved density analysis.

Findings

Derivation of DRGEs for correlation functions.

Application of DRGEs to relate high and low-density liquid properties.

Framework for calculating liquid properties at various densities.

Abstract

We study response of liquid to a scale transformation, which generates a change of the liquid density, and obtain a set of differential equations for correlation functions. The set of equations, which we call density renormalization group equations (DRGEs), is similar to the BBGKY hierarchy as it relates different multiple-point correlation functions. In particular, we derive DRGEs for one-particle irreducible vertex functions of liquid by performing Legendre transformations, which enables us to calculate properties of liquid at higher density in terms of correlation functions at lower density.