---
_id: '180'
abstract:
- lang: eng
  text: In this paper we define and study the classical Uniform Electron Gas (UEG),
    a system of infinitely many electrons whose density is constant everywhere in
    space. The UEG is defined differently from Jellium, which has a positive constant
    background but no constraint on the density. We prove that the UEG arises in Density
    Functional Theory in the limit of a slowly varying density, minimizing the indirect
    Coulomb energy. We also construct the quantum UEG and compare it to the classical
    UEG at low density.
acknowledgement: "This project has received funding from the European Research Council
  (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme
  (grant agreement 694227 for R.S. and MDFT 725528 for M.L.). Financial support by
  the Austrian Science Fund (FWF), project No P 27533-N27 (R.S.) and by the US National
  Science Foundation, grant No PHY12-1265118 (E.H.L.) are gratefully acknowledged."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
  full_name: Lewi, Mathieu
  last_name: Lewi
- 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
citation:
  ama: Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron
    gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2018;5:79-116. doi:<a
    href="https://doi.org/10.5802/jep.64">10.5802/jep.64</a>
  apa: Lewi, M., Lieb, É., &#38; Seiringer, R. (2018). Statistical mechanics of the
    uniform electron gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>.
    Ecole Polytechnique. <a href="https://doi.org/10.5802/jep.64">https://doi.org/10.5802/jep.64</a>
  chicago: Lewi, Mathieu, Élliott Lieb, and Robert Seiringer. “Statistical Mechanics
    of the Uniform Electron Gas.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>.
    Ecole Polytechnique, 2018. <a href="https://doi.org/10.5802/jep.64">https://doi.org/10.5802/jep.64</a>.
  ieee: M. Lewi, É. Lieb, and R. Seiringer, “Statistical mechanics of the uniform
    electron gas,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5.
    Ecole Polytechnique, pp. 79–116, 2018.
  ista: Lewi M, Lieb É, Seiringer R. 2018. Statistical mechanics of the uniform electron
    gas. Journal de l’Ecole Polytechnique - Mathematiques. 5, 79–116.
  mla: Lewi, Mathieu, et al. “Statistical Mechanics of the Uniform Electron Gas.”
    <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5, Ecole Polytechnique,
    2018, pp. 79–116, doi:<a href="https://doi.org/10.5802/jep.64">10.5802/jep.64</a>.
  short: M. Lewi, É. Lieb, R. Seiringer, Journal de l’Ecole Polytechnique - Mathematiques
    5 (2018) 79–116.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2023-10-17T08:05:28Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.5802/jep.64
ec_funded: 1
external_id:
  arxiv:
  - '1705.10676'
file:
- access_level: open_access
  checksum: 1ba7cccdf3900f42c4f715ae75d6813c
  content_type: application/pdf
  creator: dernst
  date_created: 2018-12-17T16:38:18Z
  date_updated: 2020-07-14T12:45:16Z
  file_id: '5726'
  file_name: 2018_JournaldeLecoleMath_Lewi.pdf
  file_size: 843938
  relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: '         5'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 79 - 116
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_identifier:
  eissn:
  - 2270-518X
  issn:
  - 2429-7100
publication_status: published
publisher: Ecole Polytechnique
publist_id: '7741'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Statistical mechanics of the uniform electron gas
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2018'
...