基于量子统计第一性原理分析液体介质膜上准中性空间非均匀电荷系统的平衡态
Analyzing the equilibrium states of quasi-neutral spatially inhomogeneous system of charges above liquid dielectric film basing on first principles of quantum statistics
摘要：
建立了液体介质表面电荷的准中性平衡态理论。这个理论是基于系统的量子统计的第一原理，包括许多相同的粒子。所提出的方法涉及到应用变分原理，修改所考虑的系统，和B-Fermi模型。根据发展的理论，得到了一个自洽方程。这些方程提供了描述系统的主要参数之间的关系：静态电场的电势、电荷的分布函数和液体电介质的表面轮廓。该方程被用来研究系统中的空间周期态的相变。该方法可用于分析系统向波动型空间周期态的相变性质。采用解析和数值计算的方法，详细研究了这种相变的临界参数与液体介质膜厚度的关系。讨论了所研究系统新的非对称相的稳定性判据。
英文摘要：
The theory of quasi-neutral equilibrium states of charges above liquid dielectric surface is built. This theory is based on first principles of quantum statistics for systems, comprising many identical particles. The proposed approach is concerned with applying the variation principle, modified for the considered systems, and the Thomas-Fermi model. In terms of the developed theory a self-consistency equations are obtained. These equations provide the relation between the main parameters, describing the system: the potential of static electric field, the distribution function of charges and the surface profile of liquid dielectric. The equations are used to study the phase transition in the system to a spatially periodic state. The proposed method can be applied to analyzing the properties of the phase transition in the system to a spatially periodic states of wave type. Using the analytical and numerical methods, we make a detailed research of the dependence of critical parameters of such phase transition on the thickness of liquid dielectric film. Some stability criteria of the new asymmetric phase of the studied system are discussed.
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