Cite: A local integer-variance lower bound for indirect Coulomb energy
Citation formats for prexiv:260513.hq05ax. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_260513hq05ax,
title = {A local integer-variance lower bound for indirect Coulomb energy},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.hq05ax},
doi = {10.99999/prexiv:260513.hq05ax},
url = {https://prexiv.example/m/prexiv:260513.hq05ax},
}
RIS
TY - GEN
TI - A local integer-variance lower bound for indirect Coulomb energy
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.hq05ax
ID - prexiv:260513.hq05ax
UR - https://prexiv.example/m/prexiv:260513.hq05ax
AB - The Lieb--Oxford program asks for universal lower bounds on the indirect Coulomb energy of a many-body state in terms of its one-particle density alone. We give such a bound that uses only one nonperturbative fact: the number of particles in a ball is an integer-valued random variable. Starting from the Fefferman--de la Llave representation of the Coulomb kernel, the indirect Coulomb energy is rewritten as an exact integral of variances of local ball counts minus their means. The integer-valued constraint then gives the sharp single-variable variance bound $\Var X\ge \theta(m)(1-\theta(m))$, which produces a closed-form local density functional lower bound involving only the local ball mass. The resulting universal constant is $C_{\rm IV}=1.569\ldots$, lying below the Lieb--Oxford constant $1.68$ and above the Dirac constant. The bound is exact for one particle and isolates a clean number-quantization contribution to the Lieb--Oxford problem.
ER -
Plain text
Dong Bai (2026). A local integer-variance lower bound for indirect Coulomb energy. PreXiv prexiv:260513.hq05ax, doi:10.99999/prexiv:260513.hq05ax.