In this paper we develop a theory for the first and second sounds in a two-dimensional atomic gas across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic equations which incorporate the dynamics of the quantized vortices, rather than the conventional ones for a three-dimensional superfluid. As far as the sound dispersion equation is concerned, the modification is essentially equivalent to replacing the static superfluid density with a frequency-dependent one, renormalized by the frequency-dependent ``dielectric constant'' of the vortices. This theory has two direct consequences. First, because the renormalized superfluid density at finite frequencies does not display discontinuity across the superfluid transition, in contrast to the static superfluid density, the sound velocities vary smoothly across the transition. Second, the theory includes dissipation due to free vortices and thus naturally describes the sound-to-diffusion crossover for the second sound in the normal phase. With only one fitting parameter, our theory gives a perfect agreement with the experimental measurements of sound velocities across the transition, as well as the quality factor in the vicinity of the transition. The predictions from this theory can be further verified by future experiments.
Phenomena following a rapid mechanical quench of liquid 4He from its normal to its superfluid phase are reported and discussed. The mechanical expansion apparatus is an improved version of that described previously. It uses a double-cell geometry to effect a partial separation of the sample from the convolutions of the bellows that form the outer wall of the cell. Consistent with earlier work, no evidence is found for the production of quantized vortices via the Kibble-Zurek (KZ) mechanism. Although the expansion is complete within 15ms , the second-sound velocity and attenuation continue to increase for a further approximately 60ms ; correspondingly the temperature decreases. Subsequently, the temperature rises again toward its final value as the second-sound velocity and attenuation decrease. It is shown that this unexpected behavior is apparently associated with a large-amplitude second-sound oscillation produced by the expansion, and it is suggested that the observed vortices are created by the normal fluid-superfluid counterflow that constitutes the second-sound wave. If production of large-amplitude second sound is inherent to the mechanical expansion of liquid 4He through the superfluid transition, as appears to be the case for final temperatures more than 3mK from the lambda transition, the phenomenon sets a lower bound on the density of KZ vortices that can be detected in this type of experiment.