---
_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.'
accept: '1'
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
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
cc_license: '''https://creativecommons.org/licenses/by/4.0/'''
citation:
ama: Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute,
trapped gas at positive temperature. *Communications in Mathematical Physics*.
2019;368(2):723-776. doi:10.1007/s00220-018-3239-0
apa: 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. https://doi.org/10.1007/s00220-018-3239-0
chicago: 'Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein
Condensation in a Dilute, Trapped Gas at Positive Temperature.” *Communications
in Mathematical Physics* 368, no. 2 (2019): 723–76. https://doi.org/10.1007/s00220-018-3239-0.'
ieee: A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in
a dilute, trapped gas at positive temperature,” *Communications in Mathematical
Physics*, vol. 368, no. 2, 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.” *Communications in Mathematical Physics*, vol.
368, no. 2, Springer, 2019, pp. 723–76, doi:10.1007/s00220-018-3239-0.
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: 2020-01-21T13:22:16Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s00220-018-3239-0
file:
- access_level: open_access
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T10:34:06Z
date_updated: 2018-12-17T10:34:06Z
file_id: '5688'
file_name: 2018_CommunMathPhys_Deuchert.pdf
file_size: 893902
open_access: 1
relation: main_file
success: 1
file_date_updated: 2018-12-17T10:34:06Z
intvolume: ' 368'
issue: '2'
language:
- iso: eng
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'
status: public
title: Bose–Einstein condensation in a dilute, trapped gas at positive temperature
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 368
year: '2019'
...