Exact series expansion for even frequency moments of the dynamic structure factor

TL;DR

This paper derives an exact series expansion for even frequency moments of the dynamic structure factor and proposes truncations to evaluate moments for the finite temperature uniform electron gas, validated against Monte Carlo simulations.

Contribution

The paper introduces an exact series representation for even frequency moments and provides truncation methods for practical evaluation in electron gas models.

Findings

Series expansion accurately represents moments

Truncation methods are effective within certain parameters

Results validated against path integral Monte Carlo simulations

Abstract

An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth and fifth frequency moments for the finite temperature uniform electron gas. Their applicability range in terms of degeneracy parameter and wavenumber is determined by exploiting the non-interacting limit and by comparing with the quasi-exact results of path integral Monte Carlo simulations.