Dielectric Function and Magnetization Waves in High Magnetic Fields

Abstract

The appropriate equilibrium Wigner distribution function is calculated for a quantum plasma of electrons with spin index $\ensuremath{\sigma}$, in high magnetic fields such that $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}\ensuremath{\approx}{E}_{F}$. The quantum Vlasov equation is solved for the linear response, and there results a new form of the dielectric function $D(\mathrm{k}, \ensuremath{\omega})$ which is convenient for expansion in powers of ${{k}_{\ensuremath{\perp}}}^{2}$. It is then shown that ordinary density fluctuations produced by a longitudinal wave will be accompanied by large-amplitude magnetization waves when the quantum plasma is in its lowest state, $n=0$, $\ensuremath{\sigma}=\ensuremath{-}1$.