---
_id: '13225'
abstract:
- lang: eng
  text: Recently the leading order of the correlation energy of a Fermi gas in a coupled
    mean-field and semiclassical scaling regime has been derived, under the assumption
    of an interaction potential with a small norm and with compact support in Fourier
    space. We generalize this result to large interaction potentials, requiring only
    |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three
    dimensions. Significant improvements compared to recent work include stronger
    bounds on non-bosonizable terms and more efficient control on the bosonization
    of the kinetic energy.
acknowledgement: "RS was supported by the European Research Council under the European
  Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).
  MP acknowledges financial support from the European Research Council under the European
  Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement
  No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the
  Swiss National Science Foundation through the Grant “Dynamical and energetic properties
  of Bose-Einstein condensates” and from the European Research Council through the
  ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale
  per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research
  Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access
  funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement."
article_number: '65'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly
    interacting Fermi gas with large interaction potential. <i>Archive for Rational
    Mechanics and Analysis</i>. 2023;247(4). doi:<a href="https://doi.org/10.1007/s00205-023-01893-6">10.1007/s00205-023-01893-6</a>
  apa: Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation
    energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-023-01893-6">https://doi.org/10.1007/s00205-023-01893-6</a>
  chicago: Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer.
    “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.”
    <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a
    href="https://doi.org/10.1007/s00205-023-01893-6">https://doi.org/10.1007/s00205-023-01893-6</a>.
  ieee: N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy
    of a weakly interacting Fermi gas with large interaction potential,” <i>Archive
    for Rational Mechanics and Analysis</i>, vol. 247, no. 4. Springer Nature, 2023.
  ista: Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of
    a weakly interacting Fermi gas with large interaction potential. Archive for Rational
    Mechanics and Analysis. 247(4), 65.
  mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
    Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s00205-023-01893-6">10.1007/s00205-023-01893-6</a>.
  short: N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational
    Mechanics and Analysis 247 (2023).
date_created: 2023-07-16T22:01:08Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-12-13T11:31:14Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00205-023-01893-6
ec_funded: 1
external_id:
  arxiv:
  - '2106.13185'
  isi:
  - '001024369000001'
file:
- access_level: open_access
  checksum: 2b45828d854a253b14bf7aa196ec55e9
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  creator: dernst
  date_created: 2023-11-14T13:12:12Z
  date_updated: 2023-11-14T13:12:12Z
  file_id: '14535'
  file_name: 2023_ArchiveRationalMechAnalysis_Benedikter.pdf
  file_size: 851626
  relation: main_file
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file_date_updated: 2023-11-14T13:12:12Z
has_accepted_license: '1'
intvolume: '       247'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
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: Correlation energy of a weakly interacting Fermi gas with large interaction
  potential
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 247
year: '2023'
...
---
_id: '7900'
abstract:
- lang: eng
  text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
    systems. However, it suffers from some defects in predicting physical properties,
    making necessary a theory of quantum correlations. Recently, bosonization of many-body
    correlations has been rigorously justified as an upper bound on the correlation
    energy at high density with weak interactions. We review the bosonic approximation,
    deriving an effective Hamiltonian. We then show that for systems with Coulomb
    interaction this effective theory predicts collective excitations (plasmons) in
    accordance with the random phase approximation of Bohm and Pines, and with experimental
    observation.
article_number: '2060009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
citation:
  ama: Benedikter NP. Bosonic collective excitations in Fermi gases. <i>Reviews in
    Mathematical Physics</i>. 2021;33(1). doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>
  apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. <i>Reviews
    in Mathematical Physics</i>. World Scientific. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>
  chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>. World Scientific, 2021. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>.
  ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021.
  ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
    in Mathematical Physics. 33(1), 2060009.
  mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1, 2060009, World Scientific, 2021,
    doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>.
  short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-09-05T16:07:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
  arxiv:
  - '1910.08190'
  isi:
  - '000613313200010'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.08190
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:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7901'
abstract:
- lang: eng
  text: We derive rigorously the leading order of the correlation energy of a Fermi
    gas in a scaling regime of high density and weak interaction. The result verifies
    the prediction of the random-phase approximation. Our proof refines the method
    of collective bosonization in three dimensions. We approximately diagonalize an
    effective Hamiltonian describing approximately bosonic collective excitations
    around the Hartree–Fock state, while showing that gapless and non-collective excitations
    have only a negligible effect on the ground state energy.
acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for
  very careful reading of the paper and many helpful suggestions. NB and RS were supported
  by the European Research Council (ERC) under the European Union’s Horizon 2020 research
  and innovation programme (grant agreement No. 694227). Part of the research of NB
  was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and
  Peter Otte for explanations about the Luttinger model. PTN has received funding
  from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
  Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support
  from the European Research Council (ERC) under the European Union’s Horizon 2020
  research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901).
  BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss
  National Science Foundation through the Grant “Dynamical and energetic properties
  of Bose-Einstein condensates” and from the European Research Council through the
  ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for
  workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz
  Association). NB, PTN, BS, and RS acknowledge support for workshop participation
  from Fondation des Treilles.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Phan Thành
  full_name: Nam, Phan Thành
  last_name: Nam
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy
    of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. 2021;225:885-979.
    doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a>
  apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R.
    (2021). Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>.
    Springer. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a>
  chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
    and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.”
    <i>Inventiones Mathematicae</i>. Springer, 2021. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a>.
  ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation
    energy of a weakly interacting Fermi gas,” <i>Inventiones Mathematicae</i>, vol.
    225. Springer, pp. 885–979, 2021.
  ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation
    energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.
  mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
    Gas.” <i>Inventiones Mathematicae</i>, vol. 225, Springer, 2021, pp. 885–979,
    doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a>.
  short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones
    Mathematicae 225 (2021) 885–979.
date_created: 2020-05-28T16:48:20Z
date_published: 2021-05-03T00:00:00Z
date_updated: 2023-08-21T06:30:30Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
  arxiv:
  - '2005.08933'
  isi:
  - '000646573600001'
file:
- access_level: open_access
  checksum: f38c79dfd828cdc7f49a34b37b83d376
  content_type: application/pdf
  creator: dernst
  date_created: 2022-05-16T12:23:40Z
  date_updated: 2022-05-16T12:23:40Z
  file_id: '11386'
  file_name: 2021_InventMath_Benedikter.pdf
  file_size: 1089319
  relation: main_file
  success: 1
file_date_updated: 2022-05-16T12:23:40Z
has_accepted_license: '1'
intvolume: '       225'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 885-979
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Inventiones Mathematicae
publication_identifier:
  eissn:
  - 1432-1297
  issn:
  - 0020-9910
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi 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: 225
year: '2021'
...
---
_id: '10537'
abstract:
- lang: eng
  text: We consider the quantum many-body evolution of a homogeneous Fermi gas in
    three dimensions in the coupled semiclassical and mean-field scaling regime. We
    study a class of initial data describing collective particle–hole pair excitations
    on the Fermi ball. Using a rigorous version of approximate bosonization, we prove
    that the many-body evolution can be approximated in Fock space norm by a quasi-free
    bosonic evolution of the collective particle–hole excitations.
acknowledgement: NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM).
  RS was supported by the European Research Council (ERC) under the European Union’s
  Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was
  supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
  under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the
  European Research Council (ERC) under the European Union’s Horizon 2020 research
  and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported
  by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical
  and energetic properties of Bose-Einstein condensates,” and the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovation program
  through the ERC-AdG CLaQS (Grant Agreement No. 834782).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Phan Thành
  full_name: Nam, Phan Thành
  last_name: Nam
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic
    many-body dynamics. <i>Annales Henri Poincaré</i>. 2021. doi:<a href="https://doi.org/10.1007/s00023-021-01136-y">10.1007/s00023-021-01136-y</a>
  apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R.
    (2021). Bosonization of fermionic many-body dynamics. <i>Annales Henri Poincaré</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00023-021-01136-y">https://doi.org/10.1007/s00023-021-01136-y</a>
  chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
    and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” <i>Annales
    Henri Poincaré</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00023-021-01136-y">https://doi.org/10.1007/s00023-021-01136-y</a>.
  ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization
    of fermionic many-body dynamics,” <i>Annales Henri Poincaré</i>. Springer Nature,
    2021.
  ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Bosonization
    of fermionic many-body dynamics. Annales Henri Poincaré.
  mla: Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.”
    <i>Annales Henri Poincaré</i>, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s00023-021-01136-y">10.1007/s00023-021-01136-y</a>.
  short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri
    Poincaré (2021).
date_created: 2021-12-12T23:01:28Z
date_published: 2021-12-02T00:00:00Z
date_updated: 2023-08-17T06:19:14Z
day: '02'
department:
- _id: RoSe
doi: 10.1007/s00023-021-01136-y
ec_funded: 1
external_id:
  arxiv:
  - '2103.08224'
  isi:
  - '000725405700001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2103.08224
month: '12'
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: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonization of fermionic many-body dynamics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '6649'
abstract:
- lang: eng
  text: "While Hartree–Fock theory is well established as a fundamental approximation
    for interacting fermions, it has been unclear how to describe corrections to it
    due to many-body correlations. In this paper we start from the Hartree–Fock state
    given by plane waves and introduce collective particle–hole pair excitations.
    These pairs can be approximately described by a bosonic quadratic Hamiltonian.
    We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type
    upper bound to the ground state energy. Our result justifies the random-phase
    approximation in the mean-field scaling regime, for repulsive, regular interaction
    potentials.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Phan Thành
  full_name: Nam, Phan Thành
  last_name: Nam
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound
    for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications
    in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href="https://doi.org/10.1007/s00220-019-03505-5">10.1007/s00220-019-03505-5</a>
  apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R.
    (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
    regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-019-03505-5">https://doi.org/10.1007/s00220-019-03505-5</a>
  chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
    and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi
    Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s00220-019-03505-5">https://doi.org/10.1007/s00220-019-03505-5</a>.
  ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal
    upper bound for the correlation energy of a Fermi gas in the mean-field regime,”
    <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp.
    2097–2150, 2020.
  ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper
    bound for the correlation energy of a Fermi gas in the mean-field regime. Communications
    in Mathematical Physics. 374, 2097–2150.
  mla: Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy
    of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>,
    vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href="https://doi.org/10.1007/s00220-019-03505-5">10.1007/s00220-019-03505-5</a>.
  short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications
    in Mathematical Physics 374 (2020) 2097–2150.
date_created: 2019-07-18T13:30:04Z
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publication: Communications in Mathematical Physics
publication_identifier:
  eissn:
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  issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field
  regime
tmp:
  image: /images/cc_by.png
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---
_id: '455'
abstract:
- lang: eng
  text: The derivation of effective evolution equations is central to the study of
    non-stationary quantum many-body systems, and widely used in contexts such as
    superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry.
    We reformulate the Dirac–Frenkel approximation principle in terms of reduced density
    matrices and apply it to fermionic and bosonic many-body systems. We obtain the
    Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While
    we do not prove quantitative error estimates, our formulation does show that the
    approximation is optimal within the class of quasifree states. Furthermore, we
    prove well-posedness of the Bogoliubov–de Gennes equations in energy space and
    discuss conserved quantities
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). The authors acknowledge support by ERC Advanced Grant 321029 and
  by VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). The authors
  would like to thank Sébastien Breteaux, Enno Lenzmann, Mathieu Lewin and Jochen
  Schmid for comments and discussions about well-posedness of the Bogoliubov–de Gennes
  equations.
alternative_title:
- Annales Henri Poincare
article_processing_charge: No
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Jérémy
  full_name: Sok, Jérémy
  last_name: Sok
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Benedikter NP, Sok J, Solovej J. The Dirac–Frenkel principle for reduced density
    matrices and the Bogoliubov–de Gennes equations. <i>Annales Henri Poincare</i>.
    2018;19(4):1167-1214. doi:<a href="https://doi.org/10.1007/s00023-018-0644-z">10.1007/s00023-018-0644-z</a>
  apa: Benedikter, N. P., Sok, J., &#38; Solovej, J. (2018). The Dirac–Frenkel principle
    for reduced density matrices and the Bogoliubov–de Gennes equations. <i>Annales
    Henri Poincare</i>. Birkhäuser. <a href="https://doi.org/10.1007/s00023-018-0644-z">https://doi.org/10.1007/s00023-018-0644-z</a>
  chicago: Benedikter, Niels P, Jérémy Sok, and Jan Solovej. “The Dirac–Frenkel Principle
    for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” <i>Annales
    Henri Poincare</i>. Birkhäuser, 2018. <a href="https://doi.org/10.1007/s00023-018-0644-z">https://doi.org/10.1007/s00023-018-0644-z</a>.
  ieee: N. P. Benedikter, J. Sok, and J. Solovej, “The Dirac–Frenkel principle for
    reduced density matrices and the Bogoliubov–de Gennes equations,” <i>Annales Henri
    Poincare</i>, vol. 19, no. 4. Birkhäuser, pp. 1167–1214, 2018.
  ista: Benedikter NP, Sok J, Solovej J. 2018. The Dirac–Frenkel principle for reduced
    density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare.
    19(4), 1167–1214.
  mla: Benedikter, Niels P., et al. “The Dirac–Frenkel Principle for Reduced Density
    Matrices and the Bogoliubov–de Gennes Equations.” <i>Annales Henri Poincare</i>,
    vol. 19, no. 4, Birkhäuser, 2018, pp. 1167–214, doi:<a href="https://doi.org/10.1007/s00023-018-0644-z">10.1007/s00023-018-0644-z</a>.
  short: N.P. Benedikter, J. Sok, J. Solovej, Annales Henri Poincare 19 (2018) 1167–1214.
date_created: 2018-12-11T11:46:34Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-19T10:07:41Z
day: '01'
ddc:
- '510'
- '539'
department:
- _id: RoSe
doi: 10.1007/s00023-018-0644-z
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  - '000427578900006'
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  creator: system
  date_created: 2018-12-12T10:11:57Z
  date_updated: 2020-07-14T12:46:31Z
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  file_name: IST-2018-993-v1+1_2018_Benedikter_Dirac.pdf
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intvolume: '        19'
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issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1167 - 1214
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '7367'
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quality_controlled: '1'
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status: public
title: The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de
  Gennes equations
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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  short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
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...