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arXiv 2006.15656physics.plasm-ph
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通过第三阶张量演化方程对库仑相互作用的量子修正的流体力学:对朗缪尔波和自旋电子声波的应用

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

Pavel A. Andreev

摘要:

从传统流体力学的角度出发,通过连续性方程和欧拉方程研究等离子体中的量子效应,可以得到量子玻姆势和自旋-自旋相互作用力。然而,如果我们将流体动力学方程组扩展到13阶矩近似之外,并将三阶张量演化方程与压力演化方程一起包括在内,我们就得到了对库仑相互作用的量子修正。它被发现在自洽(平均场)近似研究的经典等离子体中的高秩张量流体动力学方程不包含相互作用的事实相反。因此,我们提出了量子流体力学模型,其中的量子效应的量子玻姆势以外的研究。发展的模型被认为是在两个区域:在等离子体中的所有电子被认为是单一的流体,和单独的自旋演化区,其中具有不同的自旋投影的电子被认为是两个不同的流体。为了说明所发现的量子效应的基本意义,我们证明了它们在朗缪尔波和自旋电子声波的光谱中的贡献。值得一提的是,压力演化方程的应用确保了压力在朗缪尔波谱中的贡献与$(3/5)v_{Fe}^{2}$成比例,这与基于连续性和欧拉方程的流体力学中出现的$(1/3)v_{Fe}^{2}$不同,其中$v_{Fe}$是费米速度。同样的修正对应于其他等离子体现象,如自旋电子声波的声速。此外,发现新的量子效应提供了新的波动解。

英文摘要:

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.

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