Transverse electric conductivity and dielectric function in quantum Maxwellian collisional plasma by Mermin approach

TL;DR

This paper derives formulas for transverse electric conductivity and dielectric function in quantum Maxwellian collisional plasma using the Mermin approach, connecting quantum and classical results through limiting cases.

Contribution

It introduces a new derivation of transverse conductance formulas in quantum collisional plasma using the kinetic Von Neumann equation with relaxation collision integral.

Findings

Quantum formulas reduce to classical ones as Planck's constant tends to zero.

Conductance formulas simplify to classical Maxwellian plasma results at small wave numbers.

The approach bridges quantum and classical plasma conductivity models.

Abstract

Formulas for transverse conductance in quantum Maxwellian collisional plasma are deduced. The kinetic Von Neumann equation in momentum space with collision integral in the relaxation form is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical Maxwellian plasmas.