Cite: The sharp kinetic--Dirac interpolation for homogeneous quasi-free fermions
Citation formats for prexiv:260513.sj9zks. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_260513sj9zks,
title = {The sharp kinetic--Dirac interpolation for homogeneous quasi-free fermions},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.sj9zks},
doi = {10.99999/prexiv:260513.sj9zks},
url = {https://prexiv.example/m/prexiv:260513.sj9zks},
}
RIS
TY - GEN
TI - The sharp kinetic--Dirac interpolation for homogeneous quasi-free fermions
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.sj9zks
ID - prexiv:260513.sj9zks
UR - https://prexiv.example/m/prexiv:260513.sj9zks
AB - What is the best exchange lower bound that the homogeneous quasi-free framework can deliver, as a function of the kinetic budget? We answer this question with a sharp constant. The bound is expressed through an explicit finite-dimensional variational function $\mathcal G_q(R)$ defined on the simplex of spin populations, and it is attained for every value of the homogeneous kinetic ratio $R\ge 1$ by spin-resolved Fermi balls, with Galilean boosts inserted when the ball configuration alone undershoots the prescribed kinetic excess. We identify the structure of the optimizer: outside the trivial regimes $R=1$ and $R\ge q^{2/3}$, every maximizer has at most two distinct positive spin densities, characterized by a quadratic Lagrange equation. A Taylor expansion of $\mathcal G_q$ at $R=1$ yields a sharp slope of $2/5$ around the unpolarized Fermi ball, refining the looser $\sqrt{R}/2$ slope of the elementary interpolation. The result resolves the quasi-free piece of the Lieb--Oxford problem exactly.
ER -
Plain text
Dong Bai (2026). The sharp kinetic--Dirac interpolation for homogeneous quasi-free fermions. PreXiv prexiv:260513.sj9zks, doi:10.99999/prexiv:260513.sj9zks.