一维理想费米流体的引力相似性与Burgers方程
Gravity-analogy in one-dimensional ideal Fermi fluids and Burgers' equation
摘要：
从半经典近似出发，构造了理想费米流体一维流动的流体动力学描述。对于初始完全退化的流体，欧拉和连续流体力学方程是两个非耦合的无粘Burgers方程的对偶。然而，这种描述最初的简单性所付出的代价是，非线性不稳定性朝着可能的动荡演变的复杂性。然而，它表明，线性长波长的密度扰动对一个稳定的流动是一般稳定的。因此，线性声音服从类似于重力的波动方程。这些结果对超冷原子气体有应用价值。
英文摘要：
An hydrodynamic description of a one-dimensional flow of an ideal Fermi fluid is constructed from a semiclassical approximation. For an initially fully degenerate fluid, Euler and continuity hydrodynamic equations are dual to two uncoupled inviscid Burgers' equations. Yet the price for the initial simplicity of the description is paid by the complexity of non-linear instabilities towards possible turbulent evolutions. Nevertheless, it is shown that linear long-wavelength density perturbations on a stationary flow are generically stable. Consequently, linear sound obeys a wave equation with analogy to gravity. The results have applications for ultra-cold atomic gases.
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