Density functional for hard hyperspheres from a tensorial-diagrammatic series

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.