Cite: A kinetic Dirac interpolation theorem for homogeneous quasi-free fermions
Citation formats for prexiv:260513.bmj5h2. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_260513bmj5h2,
title = {A kinetic Dirac interpolation theorem for homogeneous quasi-free fermions},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.bmj5h2},
doi = {10.99999/prexiv:260513.bmj5h2},
url = {https://prexiv.example/m/prexiv:260513.bmj5h2},
}
RIS
TY - GEN
TI - A kinetic Dirac interpolation theorem for homogeneous quasi-free fermions
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.bmj5h2
ID - prexiv:260513.bmj5h2
UR - https://prexiv.example/m/prexiv:260513.bmj5h2
AB - How much exchange energy can a homogeneous fermion gas concede beyond the Dirac value, and what controls the deviation? We answer this question completely within the gauge-invariant quasi-free class. The bound we obtain interpolates between the Dirac constant $C_D(q)$, attained at the unpolarized Fermi ball, and the fully spin-polarized constant $C_D(1)$, attained in the large-kinetic-excess regime. The interpolation parameter is the homogeneous kinetic ratio $R=\tau/(K_D(q)\rho^{5/3})\ge 1$, which the Pauli principle forces above unity. The proof rests on two classical inputs: the Riesz rearrangement inequality, which bounds the exchange integral by the value at indicator-of-ball occupations, and the bathtub principle, which converts the kinetic budget into a spin-polarization constraint. A short Lyapunov-style interpolation between $\ell^1$ and $\ell^{5/3}$ then yields the explicit $\sqrt{R}$ law and the small-excess slope at $R=1$. The result isolates what the quasi-free framework alone can establish about the Lieb--Oxford problem.
ER -
Plain text
Dong Bai (2026). A kinetic Dirac interpolation theorem for homogeneous quasi-free fermions. PreXiv prexiv:260513.bmj5h2, doi:10.99999/prexiv:260513.bmj5h2.