Idealized Hydrodynamics.
Idealized Hydrodynamics.
复制标题
理想化流体动力学。
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
H. Zhai
中科院分区：
文献类型：
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作者：
Zhe;Chao Gao;H. Zhai
输运是所有能量和长度尺度中最重要的物理过程之一。非相互作用玻尔兹曼方程和流体动力学方程分别描述了两个相反的输运极限。在这里，我们提出了这两个极限之间的一个意想不到的数学联系，称为extit{理想流体力学}，它指的是相互作用系统的流体动力学方程的解可以由非相互作用玻尔兹曼方程的解精确地构造出来的情况。我们分析地提供了这种理想化流体力学的三个例子。这些例子分别恢复了一维超流体中的暗孤子解，将费米化推广到强相互作用系统的流体动力学中，并确定了谐波阱中完美密度振荡的特定初始条件。例如，它们可以用来解释巴黎小组最近在超冷原子气体中进行的令人困惑的实验观察，并为未来的实验做出进一步的预测。我们设想，通过系统的数值搜索，可以找到这种理想化流体力学的广泛例子，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。
Transport is one of the most important physical processes in all energy and length scales. The non-interacting Boltzmann equation and the hydrodynamic equations respectively describe two opposite limits of transport. Here we present an unexpected mathematical connection between these two limits, named extit{idealized hydrodynamics}, which refers to the situation where the solution to the hydrodynamic equations of an interacting system can be exactly constructed from the solutions of a non-interacting Boltzmann equation. We analytically provide three examples of such idealized hydrodynamics. These examples respectively recover the dark soliton solution in a one-dimensional superfluid, generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. They can be used, for instance, to explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group, and to make further predictions for future experiments. We envision that extensive examples of such idealized hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics.