平方根Klein-Gordon-Poisson方程组的波频散
Wave dispersion derived from the square-root Klein-Gordon-Poisson system
摘要：
近年来，等离子体的量子相对论模型引起了人们极大的兴趣。特别是显着的进展已经获得了通过Klein-Gordon-Maxwell系统，它提供了一个一阶的量子等离子体的相对论制度的方法。只要等离子体自旋动力学不是一个基本的方面，它是一个可靠的方法，需要使用更精细（和更重）的模型，包括保利-薛定谔或狄拉克方程。在这项工作中，进一步简化被认为是追溯到早期的相对论性量子理论。也就是说，我们重新访问的平方根Klein-Gordon-Poisson系统，其中的相对论性能量动量关系的正分支映射到一个量子波动方程。相关的线性波的传播进行了分析，并在文献中的结果进行比较。我们确定的物理参数，同时量子和相对论效应可以在弱耦合静电等离子体中是显而易见的。
英文摘要：
Recently there has been great interest around quantum relativistic models for plasmas. In particular striking advances have been obtained by means of the Klein-Gordon-Maxwell system, which provides a first order approach to the relativistic regimes of quantum plasmas. It is a reliable method as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli-Schrödinger or Dirac equations. In this work a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein-Gordon-Poisson system, where the positive branch of the relativistic energy-momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared to the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas.
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