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The theory of quasi-neutral equilibrium states of charges above liquiddielectric surface is built. This theory is based on first principles ofquantum statistics for systems, comprising many identical particles. Theproposed approach is concerned with applying the variation principle, modifiedfor the considered systems, and the Thomas-Fermi model. In terms of thedeveloped theory a self-consistency equations are obtained. These equationsprovide the relation between the main parameters, describing the system: thepotential of static electric field, the distribution function of charges andthe surface profile of liquid dielectric. The equations are used to study thephase transition in the system to a spatially periodic state. The proposedmethod can be applied to analyzing the properties of the phase transition inthe system to a spatially periodic states of wave type. Using the analyticaland numerical methods, we make a detailed research of the dependence ofcritical parameters of such phase transition on the thickness of liquiddielectric film. Some stability criteria of the new asymmetric phase of thestudied system are discussed.

journal of physics. a, mathematical and theoretical

Analyzing the equilibrium states of quasi-neutral spatially  inhomogeneous system of charges above liquid dielectric film basing on first  principles of quantum statistics