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. In particular, 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 weight, diameter, and number of layers of particles.