论文标题
流体动力学的不确定性关系
Uncertainty Relations in Hydrodynamics
论文作者
论文摘要
流体动力学中的不确定性关系进行了数值研究。我们首先审查了随机变化方法（SVM）中广义不确定性关系的制定，这是由两位作者的论文[Phys。 Lett。 A382，1472（2018）]。在这种方法中，不确定性的有限最小值的起源归因于量子粒子的非差异（虚拟）轨迹，然后复制了量子力学中的肯纳德和罗伯逊 - 史克罗丁的不平等。相同的非差异轨迹应用于流体动力学中流体元素的运动。通过引入流体元素的位置和动量的标准偏差，得出了流体动力学的不确定性关系。这些即使适用于毛taevskii方程，然后再现了现场理论的不确定性关系。我们进一步研究了派生的关系，并发现液体和气体的不确定性关系的行为在质量上有所不同。这表明流体动力学的不确定性关系被用作对流体中液体和气体进行分类的标准。
The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present authors [Phys. Lett. A382, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schrödinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in hydrodynamics. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.
