On the density-density correlations of the non-interacting finite temperature electron gas

TL;DR

This paper provides detailed derivations of density-density correlation functions for a non-interacting electron gas at finite temperature, with applications in various theoretical and computational methods.

Contribution

It introduces new expressions for correlation functions and explores their applications in classical mapping, dielectric formalism, and equation-of-state modeling.

Findings

Derived novel expressions for pair correlation and structure factors.

Analyzed applications in classical mapping and dielectric formalism.

Provided insights into the thermal and dynamic properties of the electron gas.

Abstract

The density-density correlations of the non-interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic structure factor, thermal structure factor and imaginary time correlation function. Applications of these expressions in the classical mapping approach, self-consistent dielectric formalism and equation-of-state construction are analyzed in depth.