arXiv 1702.043682017-02math-phmath.MP

流体动力学守恒律中量子观测量的经典极限

The classical limit of quantum observables in the conservation laws of fluid dynamics

Petr Plecháč, Mattias Sandberg, Anders Szepessy

备注：: 31 pages. The solution of the nonlinear eigenvalue problem, previously based on the Cauchy-Kovalevskaya theorem, is replaced by an approximate solution in (5.3)

摘要：

在经典的工作欧文和Zwanzig [欧文J.H.和Zwanzig R.W.，J.Chem.Phys.19（1951），1173-1180 ]已经表明，宏观密度、动量和能量的量子可观测量满足流体动力学的守恒定律。本文将Irving和Zwanzig的结果推广到一般量子粒子系统的矩阵势，导出了相应的经典分子动力学极限。矩阵公式提供了半经典极限的量子可观的守恒定律，也在温度是大的情况下相比，电子本征值的差距。守恒定律中量子观测量的经典极限对于通过分子动力学模拟确定应力张量和热流的本构关系是有用的。获得分子动力学极限的主要新步骤是：（i）通过使用非线性本征值问题对角化哈密顿量，用经典动力学精确地近似量子可观察量的动力学，（ii）通过划分一般势，应用电子本征值问题的微扰分析，定义局部能量密度，（iii）确定在几个激发电子态的情况下的分子动力学应力张量和热通量，以及（iv）构造初始粒子相空间密度作为由初始守恒变量确定的局部巨正则量子系综。

英文摘要：

In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J. Chem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables for macroscopic density, momentum and energy satisfy the conservation laws of fluid dynamics. This work derives the corresponding classical molecular dynamics limit by extending Irving and Zwanzig's result to matrix-valued potentials for a general quantum particle system. The matrix formulation provides the semi-classical limit of the quantum observables in the conservation laws, also in the case where the temperature is large compared to the electron eigenvalue gaps. The classical limit of the quantum observables in the conservation laws is useful in order to determine the constitutive relations for the stress tensor and the heat flux by molecular dynamics simulations. The main new steps to obtain the molecular dynamics limit is to: (i) approximate the dynamics of quantum observables accurately by classical dynamics, by diagonalizing the Hamiltonian using a non linear eigenvalue problem, (ii) define the local energy density by partitioning a general potential, applying perturbation analysis of the electron eigenvalue problem, (iii) determine the molecular dynamics stress tensor and heat flux in the case of several excited electron states, and (iv) construct the initial particle phase-space density as a local grand canonical quantum ensemble determined by the initial conservation variables.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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