Transverse electric conductivity in quantum degenerate collisional plasma in Mermin approach

TL;DR

This paper derives formulas for transverse conductance in quantum collisional plasma using the Mermin approach, connecting quantum and classical results and analyzing the collisionless limit.

Contribution

It introduces a new derivation of transverse conductance formulas in quantum collisional plasma within the Mermin framework, bridging quantum and classical regimes.

Findings

Derived formulas reduce to classical conductance as Planck's constant approaches zero.

Conductance formulas converge to Lindhard's result in the collisionless limit.

The kinetic equation approach effectively models quantum collisional plasma behavior.

Abstract

Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach 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 electron collision frequency tends to null (i.e. plasma becomes collisionless), the conductance formula transfers in the known formula inferred earlier by Lindhard.