---
_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.
date_created: 2023-01-15T23:00:52Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-08-16T11:34:03Z
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'
...
---
_id: '7685'
abstract:
- lang: eng
  text: We consider a gas of interacting bosons trapped in a box of side length one
    in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s
    prediction for the ground state energy and the low-energy excitation spectrum.
    This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.
article_number: '2060006'
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
citation:
  ama: Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href="https://doi.org/10.1142/S0129055X20600065">10.1142/S0129055X20600065</a>
  apa: Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. <i>Reviews in Mathematical Physics</i>. World Scientific. <a href="https://doi.org/10.1142/S0129055X20600065">https://doi.org/10.1142/S0129055X20600065</a>
  chicago: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
    Regime.” <i>Reviews in Mathematical Physics</i>. World Scientific, 2021. <a href="https://doi.org/10.1142/S0129055X20600065">https://doi.org/10.1142/S0129055X20600065</a>.
  ieee: C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific,
    2021.
  ista: Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. Reviews in Mathematical Physics. 33(1), 2060006.
  mla: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
    Regime.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060006, World
    Scientific, 2021, doi:<a href="https://doi.org/10.1142/S0129055X20600065">10.1142/S0129055X20600065</a>.
  short: C. Boccato, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-04-26T22:00:45Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T10:50:13Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/S0129055X20600065
ec_funded: 1
external_id:
  arxiv:
  - '2001.00497'
  isi:
  - '000613313200007'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2001.00497
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2021'
...
---
_id: '8042'
abstract:
- lang: eng
  text: We consider systems of N bosons in a box of volume one, interacting through
    a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for
    sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov
    theory, identifying the ground state energy and the low-lying excitation spectrum
    up to errors that vanish in the limit of large N.
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: Christian
  full_name: Brennecke, Christian
  last_name: Brennecke
- first_name: Serena
  full_name: Cenatiempo, Serena
  last_name: Cenatiempo
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
citation:
  ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of
    Bose gases interacting through singular potentials. <i>Journal of the European
    Mathematical Society</i>. 2020;22(7):2331-2403. doi:<a href="https://doi.org/10.4171/JEMS/966">10.4171/JEMS/966</a>
  apa: Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). The excitation
    spectrum of Bose gases interacting through singular potentials. <i>Journal of
    the European Mathematical Society</i>. European Mathematical Society. <a href="https://doi.org/10.4171/JEMS/966">https://doi.org/10.4171/JEMS/966</a>
  chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
    “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.”
    <i>Journal of the European Mathematical Society</i>. European Mathematical Society,
    2020. <a href="https://doi.org/10.4171/JEMS/966">https://doi.org/10.4171/JEMS/966</a>.
  ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum
    of Bose gases interacting through singular potentials,” <i>Journal of the European
    Mathematical Society</i>, vol. 22, no. 7. European Mathematical Society, pp. 2331–2403,
    2020.
  ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum
    of Bose gases interacting through singular potentials. Journal of the European
    Mathematical Society. 22(7), 2331–2403.
  mla: Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting
    through Singular Potentials.” <i>Journal of the European Mathematical Society</i>,
    vol. 22, no. 7, European Mathematical Society, 2020, pp. 2331–403, doi:<a href="https://doi.org/10.4171/JEMS/966">10.4171/JEMS/966</a>.
  short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European
    Mathematical Society 22 (2020) 2331–2403.
date_created: 2020-06-29T07:59:35Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-22T07:47:04Z
day: '01'
department:
- _id: RoSe
doi: 10.4171/JEMS/966
external_id:
  arxiv:
  - '1704.04819'
  isi:
  - '000548174700006'
intvolume: '        22'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1704.04819
month: '07'
oa: 1
oa_version: Preprint
page: 2331-2403
publication: Journal of the European Mathematical Society
publication_identifier:
  issn:
  - '14359855'
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of Bose gases interacting through singular potentials
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2020'
...
---
_id: '6906'
abstract:
- lang: eng
  text: We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime.
    We show that low-energy states exhibit complete Bose–Einstein condensation with
    an optimal bound on the number of orthogonal excitations. This extends recent
    results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing
    the assumption of small interaction potential.
acknowledgement: "We would like to thank P. T. Nam and R. Seiringer for several useful
  discussions and\r\nfor suggesting us to use the localization techniques from [9].
  C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under
  the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges
  support from the NCCR SwissMAP and from the Swiss National Foundation of Science
  (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties
  of Bose–Einstein condensates”."
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: Christian
  full_name: Brennecke, Christian
  last_name: Brennecke
- first_name: Serena
  full_name: Cenatiempo, Serena
  last_name: Cenatiempo
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
citation:
  ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein
    condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical
    Physics</i>. 2020;376:1311-1395. doi:<a href="https://doi.org/10.1007/s00220-019-03555-9">10.1007/s00220-019-03555-9</a>
  apa: Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). Optimal
    rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications
    in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-019-03555-9">https://doi.org/10.1007/s00220-019-03555-9</a>
  chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
    “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.”
    <i>Communications in Mathematical Physics</i>. Springer, 2020. <a href="https://doi.org/10.1007/s00220-019-03555-9">https://doi.org/10.1007/s00220-019-03555-9</a>.
  ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for
    Bose-Einstein condensation in the Gross-Pitaevskii regime,” <i>Communications
    in Mathematical Physics</i>, vol. 376. Springer, pp. 1311–1395, 2020.
  ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein
    condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics.
    376, 1311–1395.
  mla: Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the
    Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>, vol.
    376, Springer, 2020, pp. 1311–95, doi:<a href="https://doi.org/10.1007/s00220-019-03555-9">10.1007/s00220-019-03555-9</a>.
  short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical
    Physics 376 (2020) 1311–1395.
date_created: 2019-09-24T17:30:59Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2024-02-22T13:33:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-019-03555-9
ec_funded: 1
external_id:
  arxiv:
  - '1812.03086'
  isi:
  - '000536053300012'
intvolume: '       376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1812.03086
month: '06'
oa: 1
oa_version: Preprint
page: 1311-1395
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Communications in Mathematical Physics
publication_identifier:
  eissn:
  - 1432-0916
  issn:
  - 0010-3616
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2020'
...
---
_id: '7413'
abstract:
- lang: eng
  text: We consider Bose gases consisting of N particles trapped in a box with volume
    one and interacting through a repulsive potential with scattering length of order
    N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy
    excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s
    predictions.
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: Christian
  full_name: Brennecke, Christian
  last_name: Brennecke
- first_name: Serena
  full_name: Cenatiempo, Serena
  last_name: Cenatiempo
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
citation:
  ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii
    limit. <i>Acta Mathematica</i>. 2019;222(2):219-335. doi:<a href="https://doi.org/10.4310/acta.2019.v222.n2.a1">10.4310/acta.2019.v222.n2.a1</a>
  apa: Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2019). Bogoliubov
    theory in the Gross–Pitaevskii limit. <i>Acta Mathematica</i>. International Press
    of Boston. <a href="https://doi.org/10.4310/acta.2019.v222.n2.a1">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>
  chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
    “Bogoliubov Theory in the Gross–Pitaevskii Limit.” <i>Acta Mathematica</i>. International
    Press of Boston, 2019. <a href="https://doi.org/10.4310/acta.2019.v222.n2.a1">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>.
  ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory
    in the Gross–Pitaevskii limit,” <i>Acta Mathematica</i>, vol. 222, no. 2. International
    Press of Boston, pp. 219–335, 2019.
  ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in
    the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.
  mla: Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.”
    <i>Acta Mathematica</i>, vol. 222, no. 2, International Press of Boston, 2019,
    pp. 219–335, doi:<a href="https://doi.org/10.4310/acta.2019.v222.n2.a1">10.4310/acta.2019.v222.n2.a1</a>.
  short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222
    (2019) 219–335.
date_created: 2020-01-30T09:30:41Z
date_published: 2019-06-07T00:00:00Z
date_updated: 2023-09-06T15:24:31Z
day: '07'
department:
- _id: RoSe
doi: 10.4310/acta.2019.v222.n2.a1
external_id:
  arxiv:
  - '1801.01389'
  isi:
  - '000495865300001'
intvolume: '       222'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1801.01389
month: '06'
oa: 1
oa_version: Preprint
page: 219-335
publication: Acta Mathematica
publication_identifier:
  eissn:
  - 1871-2509
  issn:
  - 0001-5962
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov theory in the Gross–Pitaevskii limit
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 222
year: '2019'
...