Title: On the spatially periodic ordering in the system of electrons above the surface of liquid helium in an external electric field
Author(s):

	D.M. Lytvynenko (National Science Center Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine; Kharkiv V.N. Karazin National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine) ,
	Yu.V. Slyusarenko (National Science Center Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine; Kharkiv V.N. Karazin National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine) ,
	A.I. Kirdin (National Science Center Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine)

A theory of equilibrium states of electrons above a liquid helium surface in the presence of an external clamping field is built based on the first principles of quantum statistics for the system of many identical Fermi-particles. The approach is based on the variation principle modified for the considered system and on Thomas-Fermi model. In terms of the developed theory we obtain the self-consistency equations that connect the parameters of the system description, i.e., the potential of a static electric field, the distribution function of electrons and the surface profile of a liquid dielectric. The equations are used to study the phase transition of the system to a spatially periodic state. To demonstrate the capabilities of the proposed method, the characteristics of the phase transition of the system to a spatially periodic state of a trough type are analyzed.

Key words: electrons, gas-liquid interfaces, variational approach, perturbation theory, phase transitions
PACS: 64.60.Ai, 73.20.At

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