Density functional for hard hyperspheres from a tensorial-diagrammatic series

TL;DR

This paper develops a tensorial diagrammatic series to represent the free energy functional for hard hyperspheres, successfully reproducing known functionals in lower dimensions and improving bulk fluid descriptions in higher dimensions.

Contribution

It introduces a novel tensorial diagrammatic approach to derive free energy functionals for hard hyperspheres across dimensions, unifying and extending existing theories.

Findings

Reproduces Percus' exact functional in 1D

Derives Kierlik-Rosinberg form in 3D

Provides better bulk fluid descriptions in 5D

Abstract

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of fundamental measures theory in three dimensions. In five dimensions, the functional describes bulk fluids better than Percus-Yevick theory does. At planar walls density profiles oscillate with smaller periods than in lower dimensions. Our findings open up avenues for treating both more general high-dimensional systems, as well as three-dimensional mixtures via dimensional reduction.