Semi-relativistic hydrodynamics of three-dimensional and low-dimensional quantum plasma

TL;DR

This paper develops semi-relativistic quantum hydrodynamic equations for three-dimensional and two-dimensional plasmas, analyzing the effects of current-current, Darwin interactions, and weak-relativistic energy additions on wave dispersion.

Contribution

It introduces a semi-relativistic quantum hydrodynamic framework for low-dimensional plasmas, including new effects of Darwin and current-current interactions.

Findings

Dispersion relations for semi-relativistic Langmuir waves are derived.

Force fields from Darwin interaction and relativistic energy are partially canceled.

Features of hydrodynamics in 2D electron gases are described.

Abstract

Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.