In this paper we develop a theory for the first and second sound 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 quantised 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, renormalised by the frequency dependent “dielectric constant” of the vortices. This theory has two direct consequences. First, because the renormalised 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. Secondly, 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.

中文翻译：

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二维超冷原子气体的动力学Kosterlitz-Thouless理论

在本文中，我们基于动态Koterlitz-Thouless理论，针对跨超流体过渡的二维原子气体中的第一和第二声音建立了理论。我们采用了一组经过修改的双流体流体动力学方程，其中包含了量化涡流的动力学，而不是传统的三维超流体动力学方程。就声音扩散方程而言，修改基本上等同于用频率相关的频率替换静态超流体密度，并通过涡旋的频率相关的“介电常数”对其重新归一化。这个理论有两个直接的后果。首先，由于与静态超流体密度相比，在有限频率处重新规范化的超流体密度不会在整个超流体过渡过程中显示出不连续性，在整个过渡过程中，声速变化平稳。其次，该理论包括由于自由涡流引起的耗散，因此自然地描述了正常相位中第二种声音的声-扩散交叉。仅需一个拟合参数，我们的理论就可以很好地与跨过渡段声速的实验测量以及过渡附近的品质因数相吻合。该理论的预测可以通过未来的实验进一步验证。我们的理论与过渡过程中声速的实验测量以及过渡附近的品质因数完全吻合。该理论的预测可以通过未来的实验进一步验证。我们的理论与过渡过程中声速的实验测量以及过渡附近的品质因数完全吻合。该理论的预测可以通过未来的实验进一步验证。