---
_id: '80'
abstract:
- lang: eng
  text: 'We consider an interacting, dilute Bose gas trapped in a harmonic potential
    at a positive temperature. The system is analyzed in a combination of a thermodynamic
    and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature
    T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering
    length is so small that the interaction energy per particle around the center
    of the trap is of the same order of magnitude as the spectral gap in the trap.
    We prove that the difference between the canonical free energy of the interacting
    gas and the one of the noninteracting system can be obtained by minimizing the
    GP energy functional. We also prove Bose–Einstein condensation in the following
    sense: The one-particle density matrix of any approximate minimizer of the canonical
    free energy functional is to leading order given by that of the noninteracting
    gas but with the free condensate wavefunction replaced by the GP minimizer.'
article_processing_charge: Yes (via OA deal)
article_type: original
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
- first_name: Jakob
  full_name: Yngvason, Jakob
  last_name: Yngvason
citation:
  ama: Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute,
    trapped gas at positive temperature. <i>Communications in Mathematical Physics</i>.
    2019;368(2):723-776. doi:<a href="https://doi.org/10.1007/s00220-018-3239-0">10.1007/s00220-018-3239-0</a>
  apa: Deuchert, A., Seiringer, R., &#38; Yngvason, J. (2019). Bose–Einstein condensation
    in a dilute, trapped gas at positive temperature. <i>Communications in Mathematical
    Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-018-3239-0">https://doi.org/10.1007/s00220-018-3239-0</a>
  chicago: Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein
    Condensation in a Dilute, Trapped Gas at Positive Temperature.” <i>Communications
    in Mathematical Physics</i>. Springer, 2019. <a href="https://doi.org/10.1007/s00220-018-3239-0">https://doi.org/10.1007/s00220-018-3239-0</a>.
  ieee: A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in
    a dilute, trapped gas at positive temperature,” <i>Communications in Mathematical
    Physics</i>, vol. 368, no. 2. Springer, pp. 723–776, 2019.
  ista: Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a
    dilute, trapped gas at positive temperature. Communications in Mathematical Physics.
    368(2), 723–776.
  mla: Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped
    Gas at Positive Temperature.” <i>Communications in Mathematical Physics</i>, vol.
    368, no. 2, Springer, 2019, pp. 723–76, doi:<a href="https://doi.org/10.1007/s00220-018-3239-0">10.1007/s00220-018-3239-0</a>.
  short: A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics
    368 (2019) 723–776.
date_created: 2018-12-11T11:44:31Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-018-3239-0
ec_funded: 1
external_id:
  isi:
  - '000467796800007'
file:
- access_level: open_access
  checksum: c7e9880b43ac726712c1365e9f2f73a6
  content_type: application/pdf
  creator: dernst
  date_created: 2018-12-17T10:34:06Z
  date_updated: 2020-07-14T12:48:07Z
  file_id: '5688'
  file_name: 2018_CommunMathPhys_Deuchert.pdf
  file_size: 893902
  relation: main_file
file_date_updated: 2020-07-14T12:48:07Z
has_accepted_license: '1'
intvolume: '       368'
isi: 1
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 723-776
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: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '7974'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bose–Einstein condensation in a dilute, trapped 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 368
year: '2019'
...