Transverse electric conductivity and dielectric permeability in quantum degenerate collisional plasma with variable collision frequency in Mermin's approach

TL;DR

This paper derives formulas for transverse electrical conductivity and dielectric permeability in quantum degenerate collisional plasma with variable collision frequency, using Mermin's approach and kinetic equations, including graphical analysis.

Contribution

It introduces a generalized approach for calculating plasma properties with arbitrary collision frequency dependence in Mermin's framework.

Findings

Formulas for transverse conductance and dielectric permeability are deduced.

Analysis of real and imaginary parts of dielectric function is provided.

Special case with collision frequency proportional to wave vector magnitude is examined.

Abstract

Formulas for transverse conductance and dielectric permeability in quantum degenerate collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. For this purpose the kinetic Shr\"{o}dinger - Boltzmann equation with collision integral of relaxation type in momentum space is applied. The case of degenerate Fermi plasma is allocated and investigated. The special case of frequency of collisions proportional to the module of a wave vector is considered. The graphic analysis of the real and imaginary parts of dielectric function is made.