By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov–Poisson–Boltzmann system around a global Maxwellian. It is shown that the electric field governed by the self-consistent Poisson equation plays a key role in the analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates of solutions to the equilibrium.

中文翻译：

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Vlasov-Poisson-Boltzmann系统的频谱分析

通过确定捕获受泊松方程控制的强迫作用的范数，我们对围绕全局麦克斯韦线性化的线性化Vlasov-Poisson-Boltzmann系统进行了详细的频谱分析。结果表明，由自洽泊松方程控制的电场在分析中起着关键作用，因此频谱结构确实不同于众所周知的玻耳兹曼方程之一。基于此，我们给出了平衡解的最佳时间衰减率。