从量子动力学理论导出的流体矩方程
Fluid moment hierarchy equations derived from quantum kinetic theory
摘要：
从静电平均场维格纳动力学方程的矩出发，导出了一组量子流体动力学方程。没有对特定的局部平衡或统计系综波函数作出任何假设。量子衍射效应只在热通量三元组的输运方程中明确出现，这是维格纳伪分布的三阶矩。导出了一般的线性色散关系，并由此恢复了长波长范围内的量子修正的玻姆-格罗斯关系。在一维情况下，非线性，行波解决方案的数值。结果揭示了量子动力学理论，Bohm-de Broglie-Madelung程函方法，和量子流体输运周围给定的平衡分布函数之间的关系。
英文摘要：
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.
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