解决低温下液氦中声传播的难题
Resolving the puzzle of sound propagation in liquid helium at low temperatures
摘要：
实验数据表明，在低于1 K的温度下，液氦中的压力与密度有立方关系。因此，声速与压力的立方根成比例。在临界压力点附近，该速度接近零，由此临界压力为负，因此指示空化不稳定状态。我们证明，要解释这种依赖性，必须将液氦视为三种量子玻色液体的混合物：稀（Gross-Pitaevskii型）玻色-爱因斯坦凝聚体，金斯堡-索比亚宁型流体和对数超流体。因此，这样的混合物的动力学描述的量子波动方程，其中不仅包含多项式（Gross-Pitaevskii和Ginzburg-Sobyanin）非线性相对于凝聚波函数，但也是一个非多项式对数非线性。我们推导出一个状态方程和声速在我们的模型，并表明它们与实验一致。
英文摘要：
Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view liquid helium as a mixture of three quantum Bose liquids: dilute (Gross-Pitaevskii-type) Bose-Einstein condensate, Ginzburg-Sobyanin-type fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (Gross-Pitaevskii and Ginzburg-Sobyanin) nonlinearities with respect to a condensate wavefunction, but also a non-polynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with experiment.
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