Features of the dielectric permittivity of the Coulomb system and the true dielectric state.

Based on the linear response theory and the diagram technique of the perturbation theory, the correlation between the homogeneous and isotropic Coulomb system permittivity features caused by the nonzero static conductivity and the effects of external electrostatic field screening is determined. The results obtained can be used to study the metal-dielectric transition at zero temperature beyond the scope of the adiabatic approximation for nuclei. It is shown that at the critical point the matter consisting of electrons and nuclei of the same type is in the "true" dielectric state characterized by the zero static conductivity and the absence of screening of the weak electrostatic field.

Second sum rule for the hot plasma permittivity.

Based on linear response theory, Kramers-Kronig relations, and diagram techniques of perturbation theory, it is shown that the second sum rule is satisfied for hot plasma permittivity. An explicit analytical expression for the second sum rule in the limit of weak nonideality is derived.

Virial theorem for an inhomogeneous medium, boundary conditions for the wave functions, and stress tensor in quantum statistics.

On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives.