Longitudinal dielectric permeability into quantum degenerate plasma with frequency of collisions proportional to the module of a wave vector

TL;DR

This paper derives formulas for the longitudinal dielectric permeability in quantum degenerate collisional plasma with collision frequency proportional to wave vector magnitude, using Mermin's approach, and compares it with non-degenerate plasma results.

Contribution

It introduces a new model for dielectric permeability with collision frequency proportional to wave vector in quantum plasma, expanding on Mermin's approach.

Findings

Dielectric function weakly depends on wave vector.

Numerical comparison shows differences between constant and variable collision frequencies.

Results applicable to quantum plasma with collisional effects.

Abstract

Formulas for the longitudinal dielectric permeability in quantum degenerate collisional plasma with the frequency of collisions proportional to the module of the wave vector, in Mermin's approach, are received. Equation of Shr\"{o}dinger - Boltzmann with integral of collisions relaxation type in Mermin's approach is applied. It is spent numerical and graphic comparison of the real and imaginary parts of dielectric function of non-degenerate and maxwellian collisional quantum plasma with a constant and a variable frequencies of collisions. It is shown, that the longitudinal dielectric function weakly depends on a wave vector.