--- _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. 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. Springer. 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. Springer, 2019. 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. 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.” 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: 2023-08-24T14:27:51Z 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 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' ...