Superfluid Theory: Vortex Theory of the Phase Transition, Pressure Dependencies in Equilibrated Three-Dimensional Bulk, and Vortex Pair Density in Quenched Two-Dimensional Film

The vortex theory of the helium-4-type superfluid phase transition, in both the 3D-bulk form and 2D-film form, is herein explained and intuitively derived. New evidence is provided supporting the accuracy of the 3D vortex loop theory in equilibrium over all pressures up to the solidification point. We show that the 3D theory consistently describes, within about 200 μK below Tλ, the pressure dependence of the helium superfluid fraction, heat capacity, vortex-loop core diameter, smallest-loop energy, and universal quantity X, which relates to an algebraic combination of the superfluid-fraction and specific-heat critical amplitudes. We suggest that the smallest vortex loops of the theory, with size on the order of angstroms, may be crude approximations for rotons. We also present a new exact analytic solution for the 2D non-equilibrium dynamics of vortex pairs in rapid temperature quenches