Lytvynenko D. Statistical theory of charged particles above dielectric surface

The dissertation is devoted to a consistent construction of the statistical approach to the description of the of charged fermion system above liquid dielectric surface in an external electric field and the phase transitions to spatially periodic structures in such systems. The variation principle is formulated, which allows to obtain a system of self-consistent equations that relates the main parameters of the system description - the distribution function of particles, the electric field potential and the profile of liquid dielectric surface. In terms of the proposed approach the expressions for the concentration of charges, electric field and potential, were obtained in the case of non-degenerate gas and in the case of going beyond Boltzmann's statistics. The applicability condition for the quasiclassical description is obtained, where going beyond the Boltzmann statistics is valid. It is shown that in the case of charged system of charges the electric field decays exponentially to a fixed value and in the quasineutral case the electric field decreases inversely proportional to the distance from the dielectric surface. The obtained concentration distribution of charges shows that the dominant part of electrons are located below the distance from the helium surface, which is comparable to the distance of a single electron the localization in the ground state above the helium surface. The phase transition critical surface depending on external electric field, temperature and the number of fermions above the dielectric surface area unit is obtained for the system of one-period structures. The order parameter of the considered phase transition being the amplitude of one-period perturbation of the liquid dielectric surface near the critical surface is obtained. It obtained order parameeter has a square root dependence on the external clamping field. In terms of the proposed approach, the equilibrium state of the electrons above a thin helium film in a quasineutral case is researched. It is shown that the available number of electrons per helium surface area unit is substantially larger than the corresponding value in the case of massive helium. It is shown that for thin helium films and large electron number above the surface area unit , their thickness does not change significantly with the further electron number growth. The possibility of periodic structures appering in such systems is shown.