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Dielectric response and structural properties of finite-temperature electron liquids

Chengliang Lin, Yong Hou, Jianmin Yuan, Yong Wu, Jianguo Wang

Abstract

The dielectric response and structural properties of finite-temperature electron liquids are central to accurately describing the physical behavior of electronic systems. This study presents a robust analytical model for the static structure factor of the uniform electron gas, combining physically motivated form for the static structure factor with constraints derived from high-accuracy path integral Monte Carlo simulations. The model accurately reproduces key features of the static structure factor across a broad range of temperatures and densities. Using this static structure factor, the density response function is directly evaluated, enabling a self-consistent definition of the static local field correction. As practical applications, the model is employed to investigate the low-velocity stopping power and the electron-ion friction coefficient. Results derived for the friction coefficient show good agreement with simulation data at moderate coupling and degeneracy. The proposed approach provides a computationally efficient and reliable method for characterizing the static response properties of correlated electron systems, facilitating improved simulations of energy deposition and ionic transport in warm dense matter and other strongly coupled quantum plasmas.

Dielectric response and structural properties of finite-temperature electron liquids

Abstract

The dielectric response and structural properties of finite-temperature electron liquids are central to accurately describing the physical behavior of electronic systems. This study presents a robust analytical model for the static structure factor of the uniform electron gas, combining physically motivated form for the static structure factor with constraints derived from high-accuracy path integral Monte Carlo simulations. The model accurately reproduces key features of the static structure factor across a broad range of temperatures and densities. Using this static structure factor, the density response function is directly evaluated, enabling a self-consistent definition of the static local field correction. As practical applications, the model is employed to investigate the low-velocity stopping power and the electron-ion friction coefficient. Results derived for the friction coefficient show good agreement with simulation data at moderate coupling and degeneracy. The proposed approach provides a computationally efficient and reliable method for characterizing the static response properties of correlated electron systems, facilitating improved simulations of energy deposition and ionic transport in warm dense matter and other strongly coupled quantum plasmas.
Paper Structure (11 sections, 32 equations, 5 figures)

This paper contains 11 sections, 32 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Theoretical method
  3. Parameters for Coulomb coupling and electron degeneracy
  4. Dielectric formulation and density response
  5. Static structure factor
  6. Low-velocity stopping power and electron-ion friction coefficient
  7. Results and discussion
  8. Parametrization of the static structure factor
  9. Static dielectric function
  10. Low-velocity stopping power and friction coefficient
  11. Conclusions

Figures (5)

  • Figure 1: Comparison of the SSF for UEG under different plasma conditions. The square, diamond, and circular symbols represent the PIMC results Dornheim2017Dornheim2020 for three degeneracy parameters $\theta=1, \theta = 2, \textrm{and } \theta = 4$ at different densities, respectively. The corresponding predictions calculated from the model proposed in this work is depicted by the red $(\theta=1)$, brown $(\theta=2)$ and blue $(\theta=4)$ lines.
  • Figure 2: Comparison of the SSF for UEG under different plasma conditions. The square symbols represent the PIMC results Dornheim2017Dornheim2020 for three densities ${r}_{ \mathrm{S}} = 10$ (panel (a)), ${r}_{ \mathrm{S}} = 50$ (panel (b)), and ${r}_{ \mathrm{S}} = 100$ (panel (c)) at the fixed degeneracy $\theta = 4$. The red lines mark the prediction obtained with the numeric strategy described in Sec. \ref{['sec:theory:ssf']}. The blue curves represent the results using the fitting formula \ref{['diameter']}.
  • Figure 3: The static response function $\chi(q)$ for ${r}_{ \mathrm{S}} = 20$ and $\theta = 4$ predicted by different approaches. The square symbols represent the PIMC data reported in Ref. Dornheim2020. The magenta, blue and red curves represent the predictions calculated using $A(q)=1$ (magenta), $A(q)=0$ (blue) and $A(q)$\ref{['aqfunc']} (red), respectively. For comparison, the results for Lindhard response function $\chi_0(q)$ (black) and the RPA response function ${\chi}_{ \mathrm{RPA}}(q)$ (brown) are also displayed.
  • Figure 4: The static response function $\chi(q)$ for a fixed density ${r}_{ \mathrm{S}} = 2$ at three degeneracy parameters (upper panel (a)) and for a fixed degeneracy $\theta = 4$ at three electron densities (lower panel (b)). The PIMC data are taken from Ref. Dornheim2022 for ${r}_{ \mathrm{S}} = 2$ in the panel (a) and from Ref. Dornheim2020 for $\theta = 4$ in the panel (b). The lines represent the results calculated using the model proposed in this work.
  • Figure 5: The reduced friction coefficient at the electron density ${r}_{ \mathrm{S}} = 4$ with varying degeneracy $\theta$. The PIMC data are taken from Ref. Moldabekov2020. The gray and magenta lines present the results from the Rayleigh model \ref{['rayleigh']} and the results based on the fit of Zwicknagel \ref{['zwicknagel']}. The predictions denoted by RPA (blue) and LFC (red) are calculated without and with the static local field correction from Eq. \ref{['frictionlfcFfunc']}, respectively.