---
_id: '13226'
abstract:
- lang: eng
  text: We consider the ground state and the low-energy excited states of a system
    of N identical bosons with interactions in the mean-field scaling regime. For
    the ground state, we derive a weak Edgeworth expansion for the fluctuations of
    bounded one-body operators, which yields corrections to a central limit theorem
    to any order in 1/N−−√. For suitable excited states, we show that the limiting
    distribution is a polynomial times a normal distribution, and that higher-order
    corrections are given by an Edgeworth-type expansion.
acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert
  Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee
  for many constructive comments. L.B. gratefully acknowledges funding from the German
  Research Foundation within the Munich Center of Quantum Science and Technology (EXC
  2111) and from the European Union’s Horizon 2020 research and innovation programme
  under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical
  Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen
  Access funding enabled and organized by Projekt DEAL."
article_number: '77'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
citation:
  ama: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas.
    <i>Letters in Mathematical Physics</i>. 2023;113(4). doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>
  apa: Bossmann, L., &#38; Petrat, S. P. (2023). Weak Edgeworth expansion for the
    mean-field Bose gas. <i>Letters in Mathematical Physics</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>
  chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>.
  ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field
    Bose gas,” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4. Springer Nature,
    2023.
  ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose
    gas. Letters in Mathematical Physics. 113(4), 77.
  mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4, 77, Springer
    Nature, 2023, doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>.
  short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).
date_created: 2023-07-16T22:01:08Z
date_published: 2023-07-03T00:00:00Z
date_updated: 2023-12-13T11:31:50Z
day: '03'
department:
- _id: RoSe
doi: 10.1007/s11005-023-01698-4
ec_funded: 1
external_id:
  arxiv:
  - '2208.00199'
  isi:
  - '001022878900002'
intvolume: '       113'
isi: 1
issue: '4'
language:
- iso: eng
month: '07'
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak Edgeworth expansion for the mean-field Bose gas
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 113
year: '2023'
...
---
_id: '11783'
abstract:
- lang: eng
  text: We consider a gas of N bosons with interactions in the mean-field scaling
    regime. We review the proof of an asymptotic expansion of its low-energy spectrum,
    eigenstates, and dynamics, which provides corrections to Bogoliubov theory to
    all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer,
    and Soffer. In addition, we derive a full asymptotic expansion of the ground state
    one-body reduced density matrix.
acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert
  Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from
  the European Union’s Horizon 2020 Research and Innovation Programme under Marie
  Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged."
article_number: '061102'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
citation:
  ama: Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose
    gas. <i>Journal of Mathematical Physics</i>. 2022;63(6). doi:<a href="https://doi.org/10.1063/5.0089983">10.1063/5.0089983</a>
  apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting
    Bose gas. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0089983">https://doi.org/10.1063/5.0089983</a>
  chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
    Bose Gas.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0089983">https://doi.org/10.1063/5.0089983</a>.
  ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose
    gas,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6. AIP Publishing,
    2022.
  ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting
    Bose gas. Journal of Mathematical Physics. 63(6), 061102.
  mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting
    Bose Gas.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6, 061102, AIP
    Publishing, 2022, doi:<a href="https://doi.org/10.1063/5.0089983">10.1063/5.0089983</a>.
  short: L. Bossmann, Journal of Mathematical Physics 63 (2022).
date_created: 2022-08-11T06:37:52Z
date_published: 2022-06-10T00:00:00Z
date_updated: 2023-08-03T12:46:28Z
day: '10'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1063/5.0089983
ec_funded: 1
external_id:
  arxiv:
  - '2203.00730'
  isi:
  - '000809648100002'
file:
- access_level: open_access
  checksum: d0d32c338c1896680174be88c70968fa
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  creator: dernst
  date_created: 2022-08-11T07:03:02Z
  date_updated: 2022-08-11T07:03:02Z
  file_id: '11784'
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intvolume: '        63'
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issue: '6'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Journal of Mathematical Physics
publication_identifier:
  eissn:
  - 1089-7658
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Low-energy spectrum and dynamics of the weakly interacting Bose gas
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: 63
year: '2022'
...
---
_id: '14890'
abstract:
- lang: eng
  text: We consider a system of N interacting bosons in the mean-field scaling regime
    and construct corrections to the Bogoliubov dynamics that approximate the true
    N-body dynamics in norm to arbitrary precision. The N-independent corrections
    are given in terms of the solutions of the Bogoliubov and Hartree equations and
    satisfy a generalized form of Wick's theorem. We determine the n-point correlation
    functions of the excitations around the condensate, as well as the reduced densities
    of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point
    functions of a quasi-free state and the solution of the Hartree equation. In this
    way, the complex problem of computing all n-point correlation functions for an
    interacting N-body system is essentially reduced to the problem of solving the
    Hartree equation and the PDEs for the Bogoliubov two-point functions.
acknowledgement: "We are grateful for the hospitality of Central China Normal University
  (CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher,
  Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges
  the support by the German Research Foundation (DFG) within the Research\r\nTraining
  Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom
  the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk
  lodowska-Curie Grant Agreement No. 754411."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
- first_name: Peter
  full_name: Pickl, Peter
  last_name: Pickl
- first_name: Avy
  full_name: Soffer, Avy
  last_name: Soffer
citation:
  ama: Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. <i>Pure
    and Applied Analysis</i>. 2021;3(4):677-726. doi:<a href="https://doi.org/10.2140/paa.2021.3.677">10.2140/paa.2021.3.677</a>
  apa: Bossmann, L., Petrat, S. P., Pickl, P., &#38; Soffer, A. (2021). Beyond Bogoliubov
    dynamics. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers.
    <a href="https://doi.org/10.2140/paa.2021.3.677">https://doi.org/10.2140/paa.2021.3.677</a>
  chicago: Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov
    Dynamics.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers,
    2021. <a href="https://doi.org/10.2140/paa.2021.3.677">https://doi.org/10.2140/paa.2021.3.677</a>.
  ieee: L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,”
    <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers,
    pp. 677–726, 2021.
  ista: Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics.
    Pure and Applied Analysis. 3(4), 677–726.
  mla: Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>,
    vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:<a href="https://doi.org/10.2140/paa.2021.3.677">10.2140/paa.2021.3.677</a>.
  short: L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis
    3 (2021) 677–726.
date_created: 2024-01-28T23:01:43Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-02-05T09:26:31Z
day: '01'
department:
- _id: RoSe
doi: 10.2140/paa.2021.3.677
ec_funded: 1
external_id:
  arxiv:
  - '1912.11004'
intvolume: '         3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.11004
month: '10'
oa: 1
oa_version: Preprint
page: 677-726
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Beyond Bogoliubov dynamics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2021'
...
---
_id: '9318'
abstract:
- lang: eng
  text: We consider a system of N bosons in the mean-field scaling regime for a class
    of interactions including the repulsive Coulomb potential. We derive an asymptotic
    expansion of the low-energy eigenstates and the corresponding energies, which
    provides corrections to Bogoliubov theory to any order in 1/N.
acknowledgement: The first author gratefully acknowledges funding from the European
  Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie
  Grant Agreement No. 754411. The third author was supported by the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
  (Grant Agreement No. 694227).
article_number: e28
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations
    for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a
    href="https://doi.org/10.1017/fms.2021.22">10.1017/fms.2021.22</a>
  apa: Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion
    of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics,
    Sigma</i>. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2021.22">https://doi.org/10.1017/fms.2021.22</a>
  chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion
    of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics,
    Sigma</i>. Cambridge University Press, 2021. <a href="https://doi.org/10.1017/fms.2021.22">https://doi.org/10.1017/fms.2021.22</a>.
  ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy
    excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>,
    vol. 9. Cambridge University Press, 2021.
  ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy
    excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.
  mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly
    Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge
    University Press, 2021, doi:<a href="https://doi.org/10.1017/fms.2021.22">10.1017/fms.2021.22</a>.
  short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2023-08-07T14:35:06Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1017/fms.2021.22
ec_funded: 1
external_id:
  isi:
  - '000634006900001'
file:
- access_level: open_access
  checksum: 17a3e6786d1e930cf0c14a880a6d7e92
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  date_created: 2021-04-12T07:15:58Z
  date_updated: 2021-04-12T07:15:58Z
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  file_size: 883851
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has_accepted_license: '1'
intvolume: '         9'
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language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Asymptotic expansion of low-energy excitations for weakly interacting bosons
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: 9
year: '2021'
...
---
_id: '8130'
abstract:
- lang: eng
  text: We study the dynamics of a system of N interacting bosons in a disc-shaped
    trap, which is realised by an external potential that confines the bosons in one
    spatial dimension to an interval of length of order ε. The interaction is non-negative
    and scaled in such a way that its scattering length is of order ε/N, while its
    range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the
    simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein
    condensation. We prove that condensation is preserved by the N-body dynamics,
    where the time-evolved condensate wave function is the solution of a two-dimensional
    non-linear equation. The strength of the non-linearity depends on the scaling
    parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger
    equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the
    scattering length of the interaction. In both cases, the coupling parameter depends
    on the confining potential.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement
  in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo
  and Nikolai Leopold are gratefully acknowledged. This work was supported by the
  German Research Foundation within the Research Training Group 1838 “Spectral Theory
  and Dynamics of Quantum Systems” and has received funding from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
citation:
  ama: Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined
    3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2020;238(11):541-606.
    doi:<a href="https://doi.org/10.1007/s00205-020-01548-w">10.1007/s00205-020-01548-w</a>
  apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00205-020-01548-w">https://doi.org/10.1007/s00205-020-01548-w</a>
  chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
    Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s00205-020-01548-w">https://doi.org/10.1007/s00205-020-01548-w</a>.
  ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol.
    238, no. 11. Springer Nature, pp. 541–606, 2020.
  ista: Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly
    confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.
  mla: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly
    Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol.
    238, no. 11, Springer Nature, 2020, pp. 541–606, doi:<a href="https://doi.org/10.1007/s00205-020-01548-w">10.1007/s00205-020-01548-w</a>.
  short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.
date_created: 2020-07-18T15:06:35Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-09-05T14:19:06Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-020-01548-w
ec_funded: 1
external_id:
  arxiv:
  - '1907.04547'
  isi:
  - '000550164400001'
file:
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  checksum: cc67a79a67bef441625fcb1cd031db3d
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  creator: dernst
  date_created: 2020-12-02T08:50:38Z
  date_updated: 2020-12-02T08:50:38Z
  file_id: '8826'
  file_name: 2020_ArchiveRatMech_Bossmann.pdf
  file_size: 942343
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file_date_updated: 2020-12-02T08:50:38Z
has_accepted_license: '1'
intvolume: '       238'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 541-606
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  eissn:
  - 1432-0673
  issn:
  - 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons
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type: journal_article
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volume: 238
year: '2020'
...
---
_id: '7508'
abstract:
- lang: eng
  text: In this paper, we introduce a novel method for deriving higher order corrections
    to the mean-field description of the dynamics of interacting bosons. More precisely,
    we consider the dynamics of N d-dimensional bosons for large N. The bosons initially
    form a Bose–Einstein condensate and interact with each other via a pair potential
    of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions
    which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision
    in powers of N−1. The approximating functions are constructed as Duhamel expansions
    of finite order in terms of the first quantised analogue of a Bogoliubov time
    evolution.
acknowledgement: "Open access funding provided by Institute of Science and Technology
  (IST Austria).\r\nL.B. gratefully acknowledges the support by the German Research
  Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics
  of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello
  Porta for helpful discussions. This project has received funding from the European
  Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant
  DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1.
  Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and
  P.P. thank A.S. for his hospitality at CCNU."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- first_name: Nataša
  full_name: Pavlović, Nataša
  last_name: Pavlović
- first_name: Peter
  full_name: Pickl, Peter
  last_name: Pickl
- first_name: Avy
  full_name: Soffer, Avy
  last_name: Soffer
citation:
  ama: Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the
    mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical
    Physics</i>. 2020;178:1362-1396. doi:<a href="https://doi.org/10.1007/s10955-020-02500-8">10.1007/s10955-020-02500-8</a>
  apa: Bossmann, L., Pavlović, N., Pickl, P., &#38; Soffer, A. (2020). Higher order
    corrections to the mean-field description of the dynamics of interacting bosons.
    <i>Journal of Statistical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s10955-020-02500-8">https://doi.org/10.1007/s10955-020-02500-8</a>
  chicago: Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order
    Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.”
    <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s10955-020-02500-8">https://doi.org/10.1007/s10955-020-02500-8</a>.
  ieee: L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections
    to the mean-field description of the dynamics of interacting bosons,” <i>Journal
    of Statistical Physics</i>, vol. 178. Springer Nature, pp. 1362–1396, 2020.
  ista: Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections
    to the mean-field description of the dynamics of interacting bosons. Journal of
    Statistical Physics. 178, 1362–1396.
  mla: Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description
    of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>,
    vol. 178, Springer Nature, 2020, pp. 1362–96, doi:<a href="https://doi.org/10.1007/s10955-020-02500-8">10.1007/s10955-020-02500-8</a>.
  short: L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics
    178 (2020) 1362–1396.
date_created: 2020-02-23T09:45:51Z
date_published: 2020-02-21T00:00:00Z
date_updated: 2023-08-18T06:37:46Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02500-8
ec_funded: 1
external_id:
  arxiv:
  - '1905.06164'
  isi:
  - '000516342200001'
file:
- access_level: open_access
  checksum: 643e230bf147e64d9cdb3f6cc573679d
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-20T09:26:46Z
  date_updated: 2020-11-20T09:26:46Z
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  file_name: 2020_JournStatPhysics_Bossmann.pdf
  file_size: 576726
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file_date_updated: 2020-11-20T09:26:46Z
has_accepted_license: '1'
intvolume: '       178'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1362-1396
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Journal of Statistical Physics
publication_identifier:
  eissn:
  - 1572-9613
  issn:
  - 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Higher order corrections to the mean-field description of the dynamics of interacting
  bosons
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  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: 178
year: '2020'
...