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

TL;DR

This paper derives formulas for longitudinal electric conductivity and dielectric permeability in quantum collisional plasma using Mermin's approach, confirming consistency with known formulas and comparing quantum and classical plasma behaviors.

Contribution

It provides detailed derivations of dielectric properties in quantum collisional plasma within Mermin's framework, including new graphical analyses and comparisons.

Findings

The derived dielectric function reduces to Lindhard's formula in the collisionless limit.

The dielectric permeability formula matches Mermin's established expression.

Graphical analysis reveals differences between quantum and classical plasma responses.

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.