---
_id: '7650'
abstract:
- lang: eng
  text: We consider a dilute, homogeneous Bose gas at positive temperature. The system
    is investigated in the Gross–Pitaevskii limit, where the scattering length a is
    so small that the interaction energy is of the same order of magnitude as the
    spectral gap of the Laplacian, and for temperatures that are comparable to the
    critical temperature of the ideal gas. We show that the difference between the
    specific free energy of the interacting system and the one of the ideal gas is
    to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system
    and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show
    that the one-particle density matrix of any approximate minimizer of the Gibbs
    free energy functional is to leading order given by the one of the ideal gas.
    This in particular proves Bose–Einstein condensation with critical temperature
    given by the one of the ideal gas to leading order. One key ingredient of our
    proof is a novel use of the Gibbs variational principle that goes hand in hand
    with the c-number substitution.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions.
  Financial support by the European Research Council (ERC) under the European Union’sHorizon
  2020 research and innovation programme (Grant Agreement No. 694227) is gratefully
  acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020
  research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
  No. 836146.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
  last_name: Deuchert
  orcid: 0000-0003-3146-6746
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at
    positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271.
    doi:<a href="https://doi.org/10.1007/s00205-020-01489-4">10.1007/s00205-020-01489-4</a>
  apa: Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous
    Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00205-020-01489-4">https://doi.org/10.1007/s00205-020-01489-4</a>
  chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
    Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s00205-020-01489-4">https://doi.org/10.1007/s00205-020-01489-4</a>.
  ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose
    gas at positive temperature,” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.
  ista: Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose
    gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6),
    1217–1271.
  mla: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous
    Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href="https://doi.org/10.1007/s00205-020-01489-4">10.1007/s00205-020-01489-4</a>.
  short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236
    (2020) 1217–1271.
corr_author: '1'
date_created: 2020-04-08T15:18:03Z
date_published: 2020-03-09T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01489-4
ec_funded: 1
external_id:
  arxiv:
  - '1901.11363'
  isi:
  - '000519415000001'
file:
- access_level: open_access
  checksum: b645fb64bfe95bbc05b3eea374109a9c
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-20T13:17:42Z
  date_updated: 2020-11-20T13:17:42Z
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  file_name: 2020_ArchRatMechanicsAnalysis_Deuchert.pdf
  file_size: 704633
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file_date_updated: 2020-11-20T13:17:42Z
fulldoi: https://doi.org/10.1007/s00205-020-01489-4
has_accepted_license: '1'
intvolume: '       236'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1217-1271
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 236
year: '2020'
...