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PreprintarXiv licencearXiv

Upper Bound on the Correlation Energy of a Dense Fermi Gas in the Thermodynamic Limit

  • Niels Benedikter
  • Sascha Lill
  • Marcello Porta
  • Benjamin Schlein
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Abstract

We prove that the random phase approximation provides an upper bound on the correlation energy of a three-dimensional, weakly interacting, Fermi gas in the thermodynamic limit at high density. More precisely, we consider a mean-field scaling regime where the kinetic and interaction Hamiltonian are scaled by ρ−2/3 and ρ−1, respectively. We use a correlated trial state constructed through a quasi-bosonic Bogoliubov transformation of collective particle--hole excitations associated to patches on the Fermi surface. Key of the proof is to control the position-space localization of the collective excitations. Combined with an iterated Duhamel expansion of the expectation values of (localized) particle number operators we obtain extensive estimates, which justify the reduction to an effective quadratic Hamiltonian and its approximate diagonalization.

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Cite

BibTeXRIS
BibTeX
@misc{benedikter2026upper,
  title = {{Upper Bound on the Correlation Energy of a Dense Fermi Gas in the Thermodynamic Limit}},
  author = {Niels Benedikter and Sascha Lill and Marcello Porta and Benjamin Schlein},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25262},
  eprint = {2610.25262},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25262},
}
RIS
TY  - UNPB
TI  - Upper Bound on the Correlation Energy of a Dense Fermi Gas in the Thermodynamic Limit
AU  - Niels Benedikter
AU  - Sascha Lill
AU  - Marcello Porta
AU  - Benjamin Schlein
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25262
UR  - https://arxiv.org/abs/2610.25262
AB  - We prove that the random phase approximation provides an upper bound on the correlation energy of a three-dimensional, weakly interacting, Fermi gas in the thermodynamic limit at high density. More precisely, we consider a mean-field scaling regime where the kinetic and interaction Hamiltonian are scaled by ρ^−2/3 and ρ^−1, respectively. We use a correlated trial state constructed through a quasi-bosonic Bogoliubov transformation of collective particle--hole excitations associated to patches on the Fermi surface. Key of the proof is to control the position-space localization of the collective excitations. Combined with an iterated Duhamel expansion of the expectation values of (localized) particle number operators we obtain extensive estimates, which justify the reduction to an effective quadratic Hamiltonian and its approximate diagonalization.
ER  -