Longitudinal dielectric permeability of the quantum degenerate collisional plasmas

TL;DR

This paper derives the dielectric permeability of quantum degenerate collisional plasmas using a kinetic equation approach, extending previous work by Mermin to include collisional effects in the relaxation approximation.

Contribution

It presents a new derivation of dielectric permeability for collisional quantum plasmas using the Wigner-Vlasov-Boltzmann kinetic equation with a relaxation collision integral.

Findings

Derived dielectric permeability for collisional quantum plasmas.

Extended Mermin's approach to include collisional effects.

Provides a theoretical framework for plasma response analysis.

Abstract

Dielectric permeability of the degenerate electronic gas for the collisional plasmas is found. The kinetic equation of Wigner -- Vlasov -- Boltzmann with integral of collisions in relaxation form in coordinate space is used. We will notice that dielectric permeability with using of the relaxation equation in the momentum space has been received by Mermin.