The Statistical Mechanical Theory of Transport Processes. V. Quantum Hydrodynamics
The Statistical Mechanical Theory of Transport Processes. V. Quantum Hydrodynamics
复制标题
传输过程的统计力学理论。
DOI：
10.1063/1.1748498
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发表时间：
1951
影响因子：
4.4
通讯作者：
R. Zwanzig
中科院分区：
文献类型：
--
作者：
J. Irving;R. Zwanzig
本文关注维格纳为处理量子统计力学问题，特别是量子力学输运过程中的问题而设计的形式技术的某些扩展。该方法是找到经典和量子统计力学之间最接近的可能类比，以便可以利用经典统计力学中的广泛工作。这种类比是通过维格纳分布函数获得的，利用维格纳分布函数可以通过相空间中的积分来计算量子力学中动态变量的平均值。我们首先阐述经典统计力学中分布函数的一些基本性质，然后阐述量子力学中密度矩阵的相应性质。我们将定义并讨论维格纳分布函数，证明它具有所需的平均特性，并获得该函数满足的刘维尔方程的模拟。我们将在简化相空间中推导出刘维尔方程的类比，然后从量子统计力学中得到流体动力学方程。
This paper is concerned with certain extensions of a formal technique devised by Wigner for handling problems in quantum‐statistical mechanics, especially to problems in quantum‐mechanical transport processes. The approach is to find the closest possible analogy between classical and quantum‐statistical mechanics, so that the extensive work in classical statistical mechanics can be utilized. This analogy is attained with the Wigner distribution function, with which averages of dynamical variables in quantum mechanics may be calculated by integrations in phase space. We will first state some basic properties of distribution functions in classical statistical mechanics, and then state the corresponding properties of the density matrix in quantum mechanics. We will define and discuss the Wigner distribution function, show that it has the desired averaging properties, and obtain the analog of the Liouville equation satisfied by this function. We will derive the analog of the Liouville equation in reduced phase space, and then obtain the equations of hydro‐dynamics from quantum‐statistical mechanics.