Density-functional theory of hard-sphere condensation under gravity

The onset of condensation of hard spheres in a gravitational field is studied using density-functional theory (DFT). We find that the local density approximation yields results identical to those obtained previously using the kinetic theory [Physica A 271, 192, (1999)], and a weighted density-functional theory gives qualitatively similar results, namely, that the temperature at which condensation begins at the bottom scales linearly with the weight, diameter, and number of layers of particles. We find also that the different DFT approaches give quantitatively different results for the density profiles at low temperatures. In particular, the weighted density-functional approach reveals the layering of hard spheres in the solid regime.