Gradient correction and Bohm potential for 2D and 1D electron gases at a finite temperature

TL;DR

This paper derives the quantum Bohm potential and density gradient correction for 2D and 1D electron gases at finite temperature, analyzing their behavior and implications for quantum plasma modeling.

Contribution

It introduces new derivations of the Bohm potential and density gradient correction for low-dimensional electron gases at finite temperature, expanding quantum hydrodynamic models.

Findings

Bohm potential behavior varies with degeneracy parameter

Density gradient correction depends on temperature and dimensionality

High-frequency Bohm potential is characterized for quantum plasmas

Abstract

From the static polarization function of electrons in the random phase approximation the quantum Bohm potential for the quantum hydrodynamic description of electrons, and the density gradient correction to the Thomas-Fermi free energy at a finite temperature for the 2D and 1D cases are derived. The behavior of the Bohm potential and of the density gradient correction as a function of the degeneracy parameter is discussed. Based on recent developments in the fluid description of quantum plasmas, the Bohm potential for the high frequency domain is presented.