Longitudinal electric conductivity and dielectric permeability in quantum plasma with constant collision frequency in Mermin' approach

Abstract

Detailed deducing of formulas for longitudinal electric conductivity and dielectric permeability in the quantum degenerate collisional plasma with constant collision frequency in Mermin' approach is given. The kinetic Schr\"{o}dinger-Boltzmann equation in momentum space in relaxation approximation is used. It is shown that when collision frequency of plasma particles tends to zero (plasma passes to collisionless one), the deduced formula for dielectric function passes to the known Lindhard' formula for collisionless plasmas. It is shown that the deduced formula for dielectric permeability coincides with known Mermin's formula. Graphic research of the real and imaginary parts of dielectric function is made. Graphic comparison of the real and imaginary parts of dielectric function for quantum and classical plasma also is made. The module of derivative dielectric function also has been investigated graphically.