Distribution function and conductivity of a system of charged particles in linear response theory: Kubo theory and the nonequilibrium statistical operator method

In the framework of Kubo theory and the nonequilibrium statistical operator (NSO) method, general expressions are obtained for the linearized distribution function that take into account exactly the interparticle interaction and are valid for arbitrary frequency $\omega$ and wave vector $\mathbf q$ of an external electric field. It is shown that the results of Kubo theory and the NSO method are equivalent for the linearized distribution function and the conductivity of a system of charged particles. A connection is established between the linearized distribution function and the electric field in the medium. An analysis of the obtained expressions in the long-wavelength limit shows that Kubo's formula for the frequency dispersion of the conductivity characterizes the response to the total field in the medium.