Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between these two limits; that is, there exist situations that the solution to a class of interacting hydrodynamic equations with certain initial conditions can be exactly constructed from the dynamics of noninteracting ideal gases. We analytically provide three such examples. The first two examples focus on scale-invariant systems, which generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. The third example recovers the dark soliton solution in a one-dimensional Bose condensate. The results can explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group and make further predictions for future experiments. We envision that extensive examples of such an ideal-gas approach to hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics.

中文翻译：

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流体动力学的理想气体方法

传输是所有能量和长度尺度中最重要的物理过程之一。理想气体和流体动力学分别是两个相反的输运极限。在这里，我们提出了这两个限制之间出乎意料的数学联系；也就是说，存在这样的情况，一类具有某些初始条件的相互作用流体动力学方程的解可以从非相互作用的理想气体的动力学中精确地构造出来。我们分析性地提供了三个这样的例子。前两个例子侧重于尺度不变系统，它将费米化推广到强相互作用系统的流体动力学，并确定谐波陷阱中完美密度振荡的特定初始条件。第三个例子恢复一维玻色凝聚中的暗孤子解。该结果可以解释巴黎小组最近对超冷原子气体进行的令人费解的实验观察，并为未来的实验做出进一步预测。我们设想可以通过系统的数值搜索找到这种流体动力学理想气体方法的广泛示例，这可以在物理学的各个子领域的不同问题中找到广泛的应用。