The quadratic density response function for non-interacting fermions at arbitrary temperature
Abstract
We develop and implement the quadratic density response function of non-interacting fermions at arbitrary temperature, frequencies, and wave vectors. Starting from a Green's function formulation, we derive the quadratic response and demonstrate its equivalence to the result obtained from the Wigner equation. We further derive the classical limit through a perturbative expansion of the Vlasov equation and demonstrate that the quantum and classical formulations agree in the high-temperature limit. We analyse the limiting behaviour with respect to wavenumber and derive the zeroth harmonic response. Two independent implementations are provided and extensively benchmarked against density-functional theory, canonical path integral Monte Carlo (PIMC), and grand canonical PIMC simulations. As the density response of the interacting electron gas is commonly modelled through the ideal response functions and approximate models for the local field correction, the presented formulation will also allow for more complete explorations of interacting systems. Especially, our efficient implementation, which evaluates the ideal static and dynamic quadratic response functions in less than 0.5 ms on a 1.3 GHz processor, will enable evaluation of quadratic corrections to integrated quantities such as interaction potentials and stopping powers in warm dense matter.
Related
- Response theory at low temperature for weakly interacting quantum spin systems
- Interacting Boson System at Finite Temperature: The treatment of the lattice calculations
- Nonlinear Response of Schwarzschild Black Holes at Arbitrary Perturbative Order
- Unimodular Gravity with Arbitrary Diffusion Function: A Dynamical System Reconstruction Approach
- Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field
BibTeX
@misc{svensson2026quadratic,
title = {{The quadratic density response function for non-interacting fermions at arbitrary temperature}},
author = {Pontus Svensson and Jan Vorberger and Zhandos A. Moldabekov and Panagiotis Tolias and Paul Hamann and Xuecheng Shao and Cheng Ma and Tobias Dornheim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29257},
eprint = {2609.29257},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29257},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The quadratic density response function for non-interacting fermions at arbitrary temperature
AU - Pontus Svensson
AU - Jan Vorberger
AU - Zhandos A. Moldabekov
AU - Panagiotis Tolias
AU - Paul Hamann
AU - Xuecheng Shao
AU - Cheng Ma
AU - Tobias Dornheim
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29257
UR - https://arxiv.org/abs/2609.29257
AB - We develop and implement the quadratic density response function of non-interacting fermions at arbitrary temperature, frequencies, and wave vectors. Starting from a Green's function formulation, we derive the quadratic response and demonstrate its equivalence to the result obtained from the Wigner equation. We further derive the classical limit through a perturbative expansion of the Vlasov equation and demonstrate that the quantum and classical formulations agree in the high-temperature limit. We analyse the limiting behaviour with respect to wavenumber and derive the zeroth harmonic response. Two independent implementations are provided and extensively benchmarked against density-functional theory, canonical path integral Monte Carlo (PIMC), and grand canonical PIMC simulations. As the density response of the interacting electron gas is commonly modelled through the ideal response functions and approximate models for the local field correction, the presented formulation will also allow for more complete explorations of interacting systems. Especially, our efficient implementation, which evaluates the ideal static and dynamic quadratic response functions in less than 0.5 ms on a 1.3 GHz processor, will enable evaluation of quadratic corrections to integrated quantities such as interaction potentials and stopping powers in warm dense matter.
ER -