Cite: A gapless kinetic-to-Dirac theorem for homogeneous occupation states
Citation formats for prexiv:260513.w6hmrb. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_260513w6hmrb,
title = {A gapless kinetic-to-Dirac theorem for homogeneous occupation states},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.w6hmrb},
doi = {10.99999/prexiv:260513.w6hmrb},
url = {https://prexiv.example/m/prexiv:260513.w6hmrb},
}
RIS
TY - GEN
TI - A gapless kinetic-to-Dirac theorem for homogeneous occupation states
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.w6hmrb
ID - prexiv:260513.w6hmrb
UR - https://prexiv.example/m/prexiv:260513.w6hmrb
AB - We prove that the Dirac exchange constant is the correct asymptotic indirect-energy lower bound, in the thermodynamic limit, for a broad class of homogeneous fermionic occupation states with controlled kinetic excess and \emph{without} any spectral gap assumption at the Fermi surface. The states considered are occupation-diagonal density matrices \(\Gamma_L\) in the plane-wave basis of a periodic box, with arbitrarily correlated occupation probabilities. Writing \(\varepsilon_L\) for the per-volume kinetic excess above the finite-volume Fermi sea, normalized by \(k_F^{2}\rho L^3\), we show that for every small \(\alpha>0\) the per-volume indirect energy is bounded below by \(-C_D(q)\rho^{4/3}-A_{q,\rho}(\alpha+\varepsilon_L/\alpha)\rho^{4/3}-o_\alpha(1)\). Optimizing in \(\alpha\) gives the interpolation \(\liminf_{L\to\infty}L^{-3}I_L(\Gamma_L)\ge -(C_D(q)+2A_{q,\rho}\sqrt{\varepsilon})\rho^{4/3}\), where \(\varepsilon=\limsup\varepsilon_L\). In particular, sub-extensive kinetic excess forces the sharp Dirac bound. The proof factors into an abstract finite shell-exchange principle and two elementary lattice-Coulomb marginal estimates
ER -
Plain text
Dong Bai (2026). A gapless kinetic-to-Dirac theorem for homogeneous occupation states. PreXiv prexiv:260513.w6hmrb, doi:10.99999/prexiv:260513.w6hmrb.