半相对论量子流体力学中的平衡方程
Balance equations in semi-relativistic quantum hydrodynamics
摘要：
量子流体力学方法已应用于量子等离子体的研究。作为我们考虑的第一步，推导经典半相对论（即。e.在简要回顾方法发展的基础上，给出了一种新的流体动力学方程（微观层次的Darwin Lagrangian方程）的数值解法。它提供了更好的区分经典和量子半相对论效应。经典方程的推导是有趣的，因为它是由一个自然的，但不是很普遍的方法。这个推导包含了微观动力学的明确平均。进一步推导了相应的量子流体力学方程。在五动量近似下得到了连续性方程、欧拉方程和能量平衡方程。结果表明，相对论修正导致存在新的量子项的力场，工作领域等的表达式中的量子玻姆势的半相对论推广得到。导出了能流的量子部分，它是能量演化方程的量子玻姆势的模拟。半相对论量子等离子体中的朗缪尔波色散对应于达尔文拉格朗日量，也被认为是半相对论效应对基本等离子体现象的贡献。
英文摘要：
Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i. e. described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the energy current, which is an analog of the quantum Bohm potential for the energy evolution equation, is derived. The Langmuir wave dispersion in semi-relativistic quantum plasmas, corresponding to the Darwin Lagrangian, is also considered to demonstrate contribution of semi-relativistic effects on basic plasma phenomenon.
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。
