Longitudinal waves in electrically polarized quantum Fermi gas: quantum hydrodynamics approximation

TL;DR

This paper extends quantum hydrodynamics to study longitudinal waves in an electrically polarized three-dimensional Fermi gas, deriving new dynamical equations and analyzing how polarization affects collective excitations.

Contribution

It develops a quantum hydrodynamics framework for polarized Fermi gases, deriving new equations and analyzing dispersion relations influenced by polarization.

Findings

Dispersion relations of collective excitations are derived.

Equilibrium polarization influences wave dispersion.

New dynamical equations for polarization dynamics are formulated.

Abstract

The method of many-particle quantum hydrodynamics has been recently developed, particularly this method has been used for an electrically polarized Bose-Einstein condensate. In this paper, we present the development of this method for an electrically polarized three dimensional Fermi gas. We derive corresponding dynamical equations: equation polarization and equation of polarization current evolution as well as the Euler and continuity equations. We study dispersion dependencies of collective excitations in a polarized Fermi gas and consider interference of an equilibrium polarization on dispersion properties.