Bifurcation of solutions with crystalline symmetry

We consider the BBGKY equation for the single particle probability density in a hard sphere system. We investigate whether there is bifurcation from the fluid phase to functions which have crystalline symmetry. We find that as the density of the fluid increases from zero, there is bifurcation in one, two, and three dimensions. The bifurcation is shown to be characteristic of metastability and in general it does not occur at the equilibrium coexistence of two phases. The direction of branching and the stability of solutions near bifurcation is also discussed.