---
OA_place: repository
OA_type: green
_id: '2362'
abstract:
- lang: eng
  text: Recent developments in the physics of low-density trapped gases make it worthwhile
    to verify old, well-known results that, while plausible, were based on perturbation
    theory and assumptions about pseudopotentials. We use and extend recently developed
    techniques to give a rigorous derivation of the asymptotic formula for the ground-state
    energy of a dilute gas of N fermions interacting with a short-range, positive
    potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa,
    where E0 is the energy of the noninteracting system and is the density. A similar
    formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this
    2D energy is not the expectation value of a density-independent pseudopotential.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Élliott
  full_name: Lieb, Élliott
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Lieb É, Seiringer R, Solovej J. Ground state energy of the low density Fermi
    gas. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. 2005;71(5).
    doi:<a href="https://doi.org/10.1103/PhysRevA.71.053605">10.1103/PhysRevA.71.053605</a>
  apa: Lieb, É., Seiringer, R., &#38; Solovej, J. (2005). Ground state energy of the
    low density Fermi gas. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevA.71.053605">https://doi.org/10.1103/PhysRevA.71.053605</a>
  chicago: Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground State Energy
    of the Low Density Fermi Gas.” <i>Physical Review A - Atomic, Molecular, and Optical
    Physics</i>. American Physical Society, 2005. <a href="https://doi.org/10.1103/PhysRevA.71.053605">https://doi.org/10.1103/PhysRevA.71.053605</a>.
  ieee: É. Lieb, R. Seiringer, and J. Solovej, “Ground state energy of the low density
    Fermi gas,” <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>,
    vol. 71, no. 5. American Physical Society, 2005.
  ista: Lieb É, Seiringer R, Solovej J. 2005. Ground state energy of the low density
    Fermi gas. Physical Review A - Atomic, Molecular, and Optical Physics. 71(5).
  mla: Lieb, Élliott, et al. “Ground State Energy of the Low Density Fermi Gas.” <i>Physical
    Review A - Atomic, Molecular, and Optical Physics</i>, vol. 71, no. 5, American
    Physical Society, 2005, doi:<a href="https://doi.org/10.1103/PhysRevA.71.053605">10.1103/PhysRevA.71.053605</a>.
  short: É. Lieb, R. Seiringer, J. Solovej, Physical Review A - Atomic, Molecular,
    and Optical Physics 71 (2005).
date_created: 2018-12-11T11:57:13Z
date_published: 2005-05-01T00:00:00Z
date_updated: 2026-08-07T09:13:21Z
day: '01'
doi: 10.1103/PhysRevA.71.053605
extern: '1'
external_id:
  arxiv:
  - abs/math-ph/0412080
fulldoi: https://doi.org/10.1103/PhysRevA.71.053605
intvolume: '        71'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0412080
month: '05'
oa: 1
oa_version: None
publication: Physical Review A - Atomic, Molecular, and Optical Physics
publication_identifier:
  issn:
  - 1094-1622
publication_status: published
publisher: American Physical Society
publist_id: '4565'
status: public
title: Ground state energy of the low density Fermi gas
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 71
year: '2005'
...