论文标题
通过第三级张量演化方程式量子校正量子的流体动力学：应用于Langmuir波和自旋电子声波
Hydrodynamics of quantum corrections to the Coulomb interaction via the third rank tensor evolution equation: Application to the Langmuir waves and the spin-electron-acoustic waves
论文作者
论文摘要
如果我们通过连续性和欧拉方程来研究传统流体动力学方面的量子效应，我们会发现量子BOHM电位和自旋旋转相互作用的力。但是，如果我们将设定的流体动力方程式扩展到13摩托的近似之外，并包括第三级张量演化方程以及压力演化方程，我们将获得库仑相互作用的量子校正。与以下事实相比，较高等级张量的流体动力方程不包含在自偏（浮力）近似中研究的经典等离子体中的相互作用。因此，我们提出量子流体动力学模型，其中研究了量子效应超出量子bohm电位。在两个方案中考虑了开发的模型：等离子体中的所有电子都被视为单流体，而单独的自旋进化状态，其中具有不同自旋投影的电子被视为两种不同的流体。为了说明发现量子效应的基本含义，我们证明了它们在Langmuir波和自旋电子声波的光谱中的贡献。值得一提的是，压力进化方程的应用确保在Langmuir波频谱中的压力贡献与$（3/5）v_ {fe}^{2} $成比例，与$（1/3）v_ {fe}^{2} $不同，从$（1/3）v_ {fe}^{2} $基于$ iSations和fe fe fe中，$} $ fer} $ v_ fe。 速度。相同的校正对应于其他等离子体现象，例如自旋电子声波的声速。此外，发现新颖的量子效应提供了新的波浪溶液。
If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic equations beyond the 13-moments approximation, and include the third rank tensor evolution equation along with the pressure evolution equation, we obtain the quantum corrections to the Coulomb interaction. It is found in contrast with the fact that hydrodynamic equations for the higher rank tensors do not contain interaction in the classic plasmas studied in the selfconsistent (meanfield) approximation. Therefore, we present the quantum hydrodynamic model, where the quantum effects are studied beyond the quantum Bohm potential. Developed model is considered in two regimes: all electrons in plasmas are considered as the single fluid, and the separate spin evolution regime, where electrons with different spin projections are considered as two different fluids. To illustrate the fundamental meaning of found quantum effects we demonstrate their contribution in the spectrum of the Langmuir waves and the spin-electron-acoustic waves. It is worth to mention that the application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to $(3/5)v_{Fe}^{2}$, unlike $(1/3)v_{Fe}^{2}$ appearing from hydrodynamics based on the continuity and Euler equations, where $v_{Fe}$ is the Fermi velocity. Same correction corresponds on other plasmas phenomena like the speed of sound for spin-electron-acoustic waves. Moreover, it is found that novel quantum effects provide the novel wave solutions.
