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arXiv · 2608.14436

A semiclassical limit of reduced Hartree-Fock theory at positive temperature

Dominic Shillingford
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Abstract

It is established that the reduced Hartree-Fock grand potential at positive temperature converges in the semiclassical limit to a Thomas-Fermi grand potential. In particular, a density-potential dual representation of the limiting functional is proposed for a general class of fermionic entropy functions. The corresponding dual problem has no duality gap and admits a maximizer. The resulting grand potential converges to the established zero-temperature grand potential as the temperature tends to zero and, for the Fermi-Dirac entropy, agrees with the standard positive-temperature Thomas-Fermi free-energy functional. The proof also establishes a semiclassical trace formula that is uniform over locally precompact families of potentials subject to a common confinement condition.

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Dominic Shillingford. 2026-08-14. A semiclassical limit of reduced Hartree-Fock theory at positive temperature. https://arxiv.org/abs/2608.14436

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