Longitudinal dielectric permeability into quantum non-degenerate and maxwellian 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 collisional plasmas with collision frequency proportional to wave vector magnitude, using Mermin's approach, and compares their behavior numerically.

Contribution

It introduces new formulas for dielectric permeability in quantum collisional plasma with variable collision frequency in Mermin's framework.

Findings

Dielectric function weakly depends on wave vector.

Numerical comparison shows differences between constant and variable collision frequencies.

Results enhance understanding of plasma response in quantum regimes.

Abstract

Formulas for the longitudinal dielectric permeability in quantum non-degenerate and maxwellian 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.