经典流体中的类量子重力波和涡旋
Quantum-like gravity waves and vortices in a classical fluid
摘要：
我们最近提出了一个新的宏观量子型实验的一般概念。它相当于通过应用类量子势将经典流体转化为量子型流体，要么直接在静止配置中，要么通过回溯循环来模拟时间演化。在这个框架中，量子势的振幅取决于普朗克常量的宏观概括，它可以在实验过程中改变，因此模拟了量子到经典的转变。该实验的例子是在这里的应用程序的这个概念的重力波在一个不可压缩的液体在一个有限高度的盆地的表面，特别强调量子化的漩涡。我们构造了一个复波函数，它以盆地中流体的高度为平方模，以速度势为相位。该波函数是超流体的典型非线性薛定谔方程的解。因此，量子势在这里被定义为流体高度的平方根。我们提出了两种将这种量子势应用于流体的方法：（i）通过表面上的力（风、鼓风机、压力、场等）的作用; (ii)盆地地面的弯曲。在最后一种情况下，基态分布产生了量子势本身，而通常只有量子力是可获得的，因此这样的实验有望提供一个量子型真空能量的宏观模型。这些结果也可能是相关的畸形波的研究，这已经被描述为非线性薛定谔方程。
英文摘要：
We have recently proposed a new general concept of macroscopic quantum-type experiment. It amounts to transform a classical fluid into a quantum-type fluid by the application of a quantum-like potential, either directly in a stationary configuration, or through a retro-active loop to simulate the time evolution. In this framework, the amplitude of the quantum potential depends on a macroscopic generalization of the Planck constant, which can be changed during the experiment, therefore simulating a quantum to classical transition. The experiment is exemplified here by an application of this concept to gravity waves at the surface of an incompressible liquid in a basin of finite height, with particular emphasis on the quantized vortex. We construct a complex wave function with the height of the fluid in the basin as its square modulus and the velocity potential as its phase. This wave function is solution of a nonlinear Schrodinger equation typical of superfluids. The quantum potential is therefore defined here in terms of the square root of the fluid height. We suggest two methods for applying this quantum-like potential to the fluid: (i) by the action of a force on the surface (wind, blower, pressure, field, etc...); (ii) by a curvature of the basin ground. In this last case the ground profile yields the quantum potential itself, while usually only the quantum force is accessible, so that such an experiment is expected to provide one with a macroscopic model of a quantum-type vacuum energy. These results may also be relevant to the study of freak waves, which have already been described by nonlinear Schrodinger equations.
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