---
_id: '12183'
abstract:
- lang: eng
  text: We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with
    Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii
    regime, with an optimal bound on the condensate depletion. Moreover, our lower
    bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann
    bracketing) a lower bound for the ground state energy of N bosons in a large box
    [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit.
acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation
  programme under the ERC grant agreement No 694227 is gratefully acknowledged.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
  full_name: Boccato, Chiara
  id: 342E7E22-F248-11E8-B48F-1D18A9856A87
  last_name: Boccato
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions.
    <i>Annales Henri Poincare</i>. 2023;24:1505-1560. doi:<a href="https://doi.org/10.1007/s00023-022-01252-3">10.1007/s00023-022-01252-3</a>
  apa: Boccato, C., &#38; Seiringer, R. (2023). The Bose Gas in a box with Neumann
    boundary conditions. <i>Annales Henri Poincare</i>. Springer Nature. <a href="https://doi.org/10.1007/s00023-022-01252-3">https://doi.org/10.1007/s00023-022-01252-3</a>
  chicago: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann
    Boundary Conditions.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a
    href="https://doi.org/10.1007/s00023-022-01252-3">https://doi.org/10.1007/s00023-022-01252-3</a>.
  ieee: C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary
    conditions,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 1505–1560,
    2023.
  ista: Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary
    conditions. Annales Henri Poincare. 24, 1505–1560.
  mla: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann
    Boundary Conditions.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature,
    2023, pp. 1505–60, doi:<a href="https://doi.org/10.1007/s00023-022-01252-3">10.1007/s00023-022-01252-3</a>.
  short: C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560.
corr_author: '1'
date_created: 2023-01-15T23:00:52Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00023-022-01252-3
ec_funded: 1
external_id:
  arxiv:
  - '2205.15284'
  isi:
  - '000910751800002'
intvolume: '        24'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2205.15284
month: '05'
oa: 1
oa_version: Preprint
page: 1505-1560
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Annales Henri Poincare
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Bose Gas in a box with Neumann boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...