Characterization of density oscillations in confined and degenerate Fermi gases

TL;DR

This paper analytically characterizes density oscillations, known as Friedel oscillations, in confined degenerate Fermi gases, providing formulas that predict oscillation properties with negligible errors under degenerate conditions.

Contribution

It introduces analytical formulas for density oscillations in confined Fermi gases, including temperature effects, enabling efficient prediction of nanoscale electron behavior.

Findings

Analytical formulas accurately describe density oscillations in degenerate Fermi gases.

Envelope functions define bounds of oscillations with negligible errors.

Results facilitate prediction of density-dependent properties in nanoscale systems.

Abstract

Friedel oscillations appear in density of Fermi gases due to Pauli exclusion principle and translational symmetry breaking nearby a defect or impurity. In confined Fermi gases, this symmetry breaking occurs also near to boundaries. Here, density oscillations of a degenerate and confined Fermi gas are considered and characterized. True nature of density oscillations are represented by analytical formulas for degenerate conditions. Analytical characterization is first done for completely degenerate case, then temperature effects are also incorporated with a finer approximation. Envelope functions defining the upper and lower bounds of these oscillations are determined. It is shown that the errors of obtained expressions are negligible as long as the system is degenerate. Numbers, amplitudes, averages and spatial coordinates of oscillations are also given by analytical expressions. The results may be helpful to efficiently predict and easily calculate the oscillations in density and density-dependent properties of confined electrons at nanoscale.