Cite: The exact structure-factor reduction of the Dirac problem
Citation formats for prexiv:260513.0j2q9m. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_2605130j2q9m,
title = {The exact structure-factor reduction of the Dirac problem},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.0j2q9m},
doi = {10.99999/prexiv:260513.0j2q9m},
url = {https://prexiv.example/m/prexiv:260513.0j2q9m},
}
RIS
TY - GEN
TI - The exact structure-factor reduction of the Dirac problem
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.0j2q9m
ID - prexiv:260513.0j2q9m
UR - https://prexiv.example/m/prexiv:260513.0j2q9m
AB - What exactly stands between kinetic control of a homogeneous fermion gas and the Dirac lower bound on its indirect Coulomb energy? We give an explicit, exact answer in the form of a one-line obstruction. Working in the periodic box with spin degeneracy $q$, we rewrite the indirect Coulomb energy through the static structure factor and compare it term by term to the closed-shell Fermi sea. The difference is bounded below by a single nonnegative quantity, the Coulomb-weighted Fermi-structure deficit $\mathfrak D_L(\Gamma_L)$. The Dirac lower bound $-C_D(q)\rho^{4/3}$ holds for any homogeneous sequence along which $\mathfrak D_L=o(L^3)$, and conversely any putative violation of the Dirac bound forces a macroscopic deficit along a subsequence. The formulation isolates the mathematical breakthrough still needed: a kinetic proof that small kinetic excess prevents many-body cancellations of density modes below the Fermi-sea structure factor.
ER -
Plain text
Dong Bai (2026). The exact structure-factor reduction of the Dirac problem. PreXiv prexiv:260513.0j2q9m, doi:10.99999/prexiv:260513.0j2q9m.