---
_id: '9891'
abstract:
- lang: eng
  text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127
    (2019)], we present a modified “floating crystal” trial state for jellium (also
    known as the classical homogeneous electron gas) with density equal to a characteristic
    function. This allows us to show that three definitions of the jellium energy
    coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache
    [“Equality of the Jellium and uniform electron gas next-order asymptotic terms
    for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb,
    and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide
    in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized
    energy” studied in a series of papers by Serfaty and others, and thus, by the
    work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate
    the jellium energy to the order n term in the logarithmic energy of n points on
    the unit 2-sphere. We improve upon known lower bounds for this renormalized energy.
    Additionally, we derive formulas for the jellium energy of periodic configurations.'
acknowledgement: The author would like to thank Robert Seiringer for guidance and
  many helpful comments on this project. The author would also like to thank Mathieu
  Lewin for his comments on the manuscript and Lorenzo Portinale for providing his
  lecture notes for the course “Mathematics of quantum many-body systems” in spring
  2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these
  lecture notes.
article_number: '083305'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
citation:
  ama: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations.
    <i>Journal of Mathematical Physics</i>. 2021;62(8). doi:<a href="https://doi.org/10.1063/5.0053494">10.1063/5.0053494</a>
  apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations.
    <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0053494">https://doi.org/10.1063/5.0053494</a>
  chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
    Configurations.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021.
    <a href="https://doi.org/10.1063/5.0053494">https://doi.org/10.1063/5.0053494</a>.
  ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,”
    <i>Journal of Mathematical Physics</i>, vol. 62, no. 8. AIP Publishing, 2021.
  ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations.
    Journal of Mathematical Physics. 62(8), 083305.
  mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium
    Configurations.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8, 083305,
    AIP Publishing, 2021, doi:<a href="https://doi.org/10.1063/5.0053494">10.1063/5.0053494</a>.
  short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).
corr_author: '1'
date_created: 2021-08-12T07:08:36Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2024-10-09T21:00:48Z
day: '01'
ddc:
- '530'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1063/5.0053494
external_id:
  arxiv:
  - '2103.07975'
  isi:
  - '000683960800003'
file:
- access_level: open_access
  checksum: d035be2b894c4d50d90ac5ce252e27cd
  content_type: application/pdf
  creator: cziletti
  date_created: 2021-10-27T12:57:06Z
  date_updated: 2021-10-27T12:57:06Z
  file_id: '10188'
  file_name: 2021_JMathPhy_Lauritsen.pdf
  file_size: 4352640
  relation: main_file
  success: 1
file_date_updated: 2021-10-27T12:57:06Z
has_accepted_license: '1'
intvolume: '        62'
isi: 1
issue: '8'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Physics
publication_identifier:
  eissn:
  - 1089-7658
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Floating Wigner crystal and periodic jellium configurations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2021'
...