Quasiequilibrium statistical mechanics of two-dimensional superfluids and the two-dimensional Coulomb gas

The virtually rigorous renormalization-group technique of Kosterlitz is applied to the vortex nucleation theory of superfluidity. The rate of decay of superfluid velocity and the superfluid density for moving helium films are obtained. The results are applicable to all temperatures on and below the critical point. Velocity exponents are directly related to the superfluid density of a film at rest. Finite-velocity effects are shown to account for pronounced changes in the dissipation and in the superfluid density near the critical point. This paper also confirms the prediction that, for a film at rest, the critical point value of $\frac{{\rho }_s}{T}$ is a universal constant. At any nonzero velocity, however, finite-velocity effects will mask this result. The subcritical static polarizability of a two-dimensional Coulomb gas with hard-core interactions is obtained, in direct analogy to the ${\rho }_s$ calculation.