---
_id: '9256'
abstract:
- lang: eng
  text: We consider the ferromagnetic quantum Heisenberg model in one dimension, for
    any spin S≥1/2. We give upper and lower bounds on the free energy, proving that
    at low temperature it is asymptotically equal to the one of an ideal Bose gas
    of magnons, as predicted by the spin-wave approximation. The trial state used
    in the upper bound yields an analogous estimate also in the case of two spatial
    dimensions, which is believed to be sharp at low temperature.
acknowledgement: "The work of MN was supported by the National Science Centre (NCN)
  Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
  (Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science
  and Technology (IST Austria)."
article_number: '31'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg
    spin chain. <i>Letters in Mathematical Physics</i>. 2021;111(2). doi:<a href="https://doi.org/10.1007/s11005-021-01375-4">10.1007/s11005-021-01375-4</a>
  apa: Napiórkowski, M. M., &#38; Seiringer, R. (2021). Free energy asymptotics of
    the quantum Heisenberg spin chain. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-021-01375-4">https://doi.org/10.1007/s11005-021-01375-4</a>
  chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics
    of the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-021-01375-4">https://doi.org/10.1007/s11005-021-01375-4</a>.
  ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum
    Heisenberg spin chain,” <i>Letters in Mathematical Physics</i>, vol. 111, no.
    2. Springer Nature, 2021.
  ista: Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum
    Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.
  mla: Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of
    the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>, vol.
    111, no. 2, 31, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s11005-021-01375-4">10.1007/s11005-021-01375-4</a>.
  short: M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).
date_created: 2021-03-21T23:01:19Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2023-08-07T14:17:00Z
day: '09'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-021-01375-4
external_id:
  isi:
  - '000626837400001'
file:
- access_level: open_access
  checksum: 687fef1525789c0950de90468dd81604
  content_type: application/pdf
  creator: dernst
  date_created: 2021-03-22T11:01:09Z
  date_updated: 2021-03-22T11:01:09Z
  file_id: '9273'
  file_name: 2021_LettersMathPhysics_Napiorkowski.pdf
  file_size: 397962
  relation: main_file
  success: 1
file_date_updated: 2021-03-22T11:01:09Z
has_accepted_license: '1'
intvolume: '       111'
isi: 1
issue: '2'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - '15730530'
  issn:
  - '03779017'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free energy asymptotics of the quantum Heisenberg spin chain
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: 111
year: '2021'
...
---
_id: '554'
abstract:
- lang: eng
  text: We analyse the canonical Bogoliubov free energy functional in three dimensions
    at low temperatures in the dilute limit. We prove existence of a first-order phase
    transition and, in the limit (Formula presented.), we determine the critical temperature
    to be (Formula presented.) to leading order. Here, (Formula presented.) is the
    critical temperature of the free Bose gas, ρ is the density of the gas and a is
    the scattering length of the pair-interaction potential V. We also prove asymptotic
    expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula
    in the limit (Formula presented.).
arxiv: 1
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robin
  full_name: Reuvers, Robin
  last_name: Reuvers
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: 'Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional
    II: The dilute Limit. <i>Communications in Mathematical Physics</i>. 2018;360(1):347-403.
    doi:<a href="https://doi.org/10.1007/s00220-017-3064-x">10.1007/s00220-017-3064-x</a>'
  apa: 'Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. (2018). The Bogoliubov
    free energy functional II: The dilute Limit. <i>Communications in Mathematical
    Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-017-3064-x">https://doi.org/10.1007/s00220-017-3064-x</a>'
  chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov
    Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical
    Physics</i>. Springer, 2018. <a href="https://doi.org/10.1007/s00220-017-3064-x">https://doi.org/10.1007/s00220-017-3064-x</a>.'
  ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy
    functional II: The dilute Limit,” <i>Communications in Mathematical Physics</i>,
    vol. 360, no. 1. Springer, pp. 347–403, 2018.'
  ista: 'Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional
    II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.'
  mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II:
    The Dilute Limit.” <i>Communications in Mathematical Physics</i>, vol. 360, no.
    1, Springer, 2018, pp. 347–403, doi:<a href="https://doi.org/10.1007/s00220-017-3064-x">10.1007/s00220-017-3064-x</a>.'
  short: M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical
    Physics 360 (2018) 347–403.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2021-01-12T08:02:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-017-3064-x
external_id:
  arxiv:
  - '1511.05953'
intvolume: '       360'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1511.05953
month: '05'
oa: 1
oa_version: Submitted Version
page: 347-403
project:
- _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_identifier:
  issn:
  - '00103616'
publication_status: published
publisher: Springer
publist_id: '7260'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'The Bogoliubov free energy functional II: The dilute Limit'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 360
year: '2018'
...
---
_id: '6002'
abstract:
- lang: eng
  text: The Bogoliubov free energy functional is analysed. The functional serves as
    a model of a translation-invariant Bose gas at positive temperature. We prove
    the existence of minimizers in the case of repulsive interactions given by a sufficiently
    regular two-body potential. Furthermore, we prove the existence of a phase transition
    in this model and provide its phase diagram.
article_processing_charge: No
arxiv: 1
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robin
  full_name: Reuvers, Robin
  last_name: Reuvers
- first_name: Jan Philip
  full_name: Solovej, Jan Philip
  last_name: Solovej
citation:
  ama: 'Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional
    I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics
    and Analysis</i>. 2018;229(3):1037-1090. doi:<a href="https://doi.org/10.1007/s00205-018-1232-6">10.1007/s00205-018-1232-6</a>'
  apa: 'Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. P. (2018). The Bogoliubov
    free energy functional I: Existence of minimizers and phase diagram. <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-018-1232-6">https://doi.org/10.1007/s00205-018-1232-6</a>'
  chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov
    Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive
    for Rational Mechanics and Analysis</i>. Springer Nature, 2018. <a href="https://doi.org/10.1007/s00205-018-1232-6">https://doi.org/10.1007/s00205-018-1232-6</a>.'
  ieee: 'M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy
    functional I: Existence of minimizers and phase diagram,” <i>Archive for Rational
    Mechanics and Analysis</i>, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.'
  ista: 'Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy
    functional I: Existence of minimizers and phase diagram. Archive for Rational
    Mechanics and Analysis. 229(3), 1037–1090.'
  mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I:
    Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:<a
    href="https://doi.org/10.1007/s00205-018-1232-6">10.1007/s00205-018-1232-6</a>.'
  short: M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics
    and Analysis 229 (2018) 1037–1090.
date_created: 2019-02-14T13:40:53Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-19T14:33:12Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-018-1232-6
external_id:
  arxiv:
  - '1511.05935'
  isi:
  - '000435367300003'
intvolume: '       229'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1511.05935
month: '09'
oa: 1
oa_version: Preprint
page: 1037-1090
project:
- _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: 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: 'The Bogoliubov free energy functional I: Existence of minimizers and phase
  diagram'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 229
year: '2018'
...
---
_id: '399'
abstract:
- lang: eng
  text: Following an earlier calculation in 3D, we calculate the 2D critical temperature
    of a dilute, translation-invariant Bose gas using a variational formulation of
    the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This
    provides the first analytical calculation of the Kosterlitz-Thouless transition
    temperature that includes the constant in the logarithm.
acknowledgement: We thank Robert Seiringer and Daniel Ueltschi for bringing the issue
  of the change in critical temperature to our attention. We also thank the Erwin
  Schrödinger Institute (all authors) and the Department of Mathematics, University
  of Copenhagen (MN) for the hospitality during the period this work was carried out.
  We gratefully acknowledge the financial support by the European Unions Seventh Framework
  Programme under the ERC Grant Agreement Nos. 321029 (JPS and RR) and 337603 (RR)
  as well as support by the VIL-LUM FONDEN via the QMATH Centre of Excellence (Grant
  No. 10059) (JPS and RR), by the National Science Center (NCN) under grant No. 2016/21/D/ST1/02430
  and the Austrian Science Fund (FWF) through project No. P 27533-N27 (MN).
article_number: '10007'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robin
  full_name: Reuvers, Robin
  last_name: Reuvers
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Napiórkowski MM, Reuvers R, Solovej J. Calculation of the critical temperature
    of a dilute Bose gas in the Bogoliubov approximation. <i>EPL</i>. 2018;121(1).
    doi:<a href="https://doi.org/10.1209/0295-5075/121/10007">10.1209/0295-5075/121/10007</a>
  apa: Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. (2018). Calculation of
    the critical temperature of a dilute Bose gas in the Bogoliubov approximation.
    <i>EPL</i>. IOP Publishing Ltd. <a href="https://doi.org/10.1209/0295-5075/121/10007">https://doi.org/10.1209/0295-5075/121/10007</a>
  chicago: Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “Calculation of
    the Critical Temperature of a Dilute Bose Gas in the Bogoliubov Approximation.”
    <i>EPL</i>. IOP Publishing Ltd., 2018. <a href="https://doi.org/10.1209/0295-5075/121/10007">https://doi.org/10.1209/0295-5075/121/10007</a>.
  ieee: M. M. Napiórkowski, R. Reuvers, and J. Solovej, “Calculation of the critical
    temperature of a dilute Bose gas in the Bogoliubov approximation,” <i>EPL</i>,
    vol. 121, no. 1. IOP Publishing Ltd., 2018.
  ista: Napiórkowski MM, Reuvers R, Solovej J. 2018. Calculation of the critical temperature
    of a dilute Bose gas in the Bogoliubov approximation. EPL. 121(1), 10007.
  mla: Napiórkowski, Marcin M., et al. “Calculation of the Critical Temperature of
    a Dilute Bose Gas in the Bogoliubov Approximation.” <i>EPL</i>, vol. 121, no.
    1, 10007, IOP Publishing Ltd., 2018, doi:<a href="https://doi.org/10.1209/0295-5075/121/10007">10.1209/0295-5075/121/10007</a>.
  short: M.M. Napiórkowski, R. Reuvers, J. Solovej, EPL 121 (2018).
date_created: 2018-12-11T11:46:15Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-08T13:30:51Z
day: '01'
department:
- _id: RoSe
doi: 10.1209/0295-5075/121/10007
external_id:
  arxiv:
  - '1706.01822'
  isi:
  - '000460003000003'
intvolume: '       121'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1706.01822
month: '01'
oa: 1
oa_version: Preprint
project:
- _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: EPL
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '7432'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov
  approximation
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 121
year: '2018'
...
---
_id: '739'
abstract:
- lang: eng
  text: We study the norm approximation to the Schrödinger dynamics of N bosons in
    with an interaction potential of the form . Assuming that in the initial state
    the particles outside of the condensate form a quasi-free state with finite kinetic
    energy, we show that in the large N limit, the fluctuations around the condensate
    can be effectively described using Bogoliubov approximation for all . The range
    of β is expected to be optimal for this large class of initial states.
article_processing_charge: No
author:
- first_name: Phan
  full_name: Nam, Phan
  id: 404092F4-F248-11E8-B48F-1D18A9856A87
  last_name: Nam
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
citation:
  ama: Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to
    mean field dynamics. <i>Journal de Mathématiques Pures et Appliquées</i>. 2017;108(5):662-688.
    doi:<a href="https://doi.org/10.1016/j.matpur.2017.05.013">10.1016/j.matpur.2017.05.013</a>
  apa: Nam, P., &#38; Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov
    correction to mean field dynamics. <i>Journal de Mathématiques Pures et Appliquées</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.matpur.2017.05.013">https://doi.org/10.1016/j.matpur.2017.05.013</a>
  chicago: Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov
    Correction to Mean Field Dynamics.” <i>Journal de Mathématiques Pures et Appliquées</i>.
    Elsevier, 2017. <a href="https://doi.org/10.1016/j.matpur.2017.05.013">https://doi.org/10.1016/j.matpur.2017.05.013</a>.
  ieee: P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction
    to mean field dynamics,” <i>Journal de Mathématiques Pures et Appliquées</i>,
    vol. 108, no. 5. Elsevier, pp. 662–688, 2017.
  ista: Nam P, Napiórkowski MM. 2017. A note on the validity of Bogoliubov correction
    to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 108(5),
    662–688.
  mla: Nam, Phan, and Marcin M. Napiórkowski. “A Note on the Validity of Bogoliubov
    Correction to Mean Field Dynamics.” <i>Journal de Mathématiques Pures et Appliquées</i>,
    vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:<a href="https://doi.org/10.1016/j.matpur.2017.05.013">10.1016/j.matpur.2017.05.013</a>.
  short: P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108
    (2017) 662–688.
date_created: 2018-12-11T11:48:15Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:52:07Z
day: '01'
department:
- _id: RoSe
doi: 10.1016/j.matpur.2017.05.013
external_id:
  isi:
  - '000414113600003'
intvolume: '       108'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1604.05240
month: '11'
oa: 1
oa_version: Submitted Version
page: 662 - 688
project:
- _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: Journal de Mathématiques Pures et Appliquées
publication_identifier:
  issn:
  - '00217824'
publication_status: published
publisher: Elsevier
publist_id: '6928'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on the validity of Bogoliubov correction to mean field dynamics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 108
year: '2017'
...
---
_id: '484'
abstract:
- lang: eng
  text: We consider the dynamics of a large quantum system of N identical bosons in
    3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed
    0 = β &lt; 1/3 and large N, we obtain a norm approximation to the many-body evolution
    in the Nparticle Hilbert space. The leading order behaviour of the dynamics is
    determined by Hartree theory while the second order is given by Bogoliubov theory.
author:
- first_name: Phan
  full_name: Nam, Phan
  id: 404092F4-F248-11E8-B48F-1D18A9856A87
  last_name: Nam
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
citation:
  ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of
    interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):683-738.
    doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">10.4310/ATMP.2017.v21.n3.a4</a>
  apa: Nam, P., &#38; Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
    dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>
  chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
    Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>.
    International Press, 2017. <a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>.
  ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
    of interacting bosons,” <i>Advances in Theoretical and Mathematical Physics</i>,
    vol. 21, no. 3. International Press, pp. 683–738, 2017.
  ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics
    of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3),
    683–738.
  mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field
    Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>,
    vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:<a href="https://doi.org/10.4310/ATMP.2017.v21.n3.a4">10.4310/ATMP.2017.v21.n3.a4</a>.
  short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics
    21 (2017) 683–738.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:58Z
day: '01'
department:
- _id: RoSe
doi: 10.4310/ATMP.2017.v21.n3.a4
ec_funded: 1
intvolume: '        21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1509.04631
month: '01'
oa: 1
oa_version: Submitted Version
page: 683 - 738
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
- _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: Advances in Theoretical and Mathematical Physics
publication_identifier:
  issn:
  - '10950761'
publication_status: published
publisher: International Press
publist_id: '7336'
quality_controlled: '1'
scopus_import: 1
status: public
title: Bogoliubov correction to the mean-field dynamics of interacting bosons
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '1545'
abstract:
- lang: eng
  text: We provide general conditions for which bosonic quadratic Hamiltonians on
    Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover
    the case when quantum systems have infinite degrees of freedom and the associated
    one-body kinetic and paring operators are unbounded. Our sufficient conditions
    are optimal in the sense that they become necessary when the relevant one-body
    operators commute.
acknowledgement: We thank Jan Dereziński for several inspiring discussions and useful
  remarks. We thank the referee for helpful comments. J.P.S. thanks the Erwin Schrödinger
  Institute for the hospitality during the thematic programme “Quantum many-body systems,
  random matrices, and disorder”. We gratefully acknowledge the financial supports
  by the European Union's Seventh Framework Programme under the ERC Advanced Grant
  ERC-2012-AdG 321029 (J.P.S.) and the REA grant agreement No. 291734 (P.T.N.), as
  well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185
  and the Austrian Science Fund (FWF) project No. P 27533-N27 (M.N.).
author:
- first_name: Phan
  full_name: Nam, Phan
  id: 404092F4-F248-11E8-B48F-1D18A9856A87
  last_name: Nam
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Nam P, Napiórkowski MM, Solovej J. Diagonalization of bosonic quadratic Hamiltonians
    by Bogoliubov transformations. <i>Journal of Functional Analysis</i>. 2016;270(11):4340-4368.
    doi:<a href="https://doi.org/10.1016/j.jfa.2015.12.007">10.1016/j.jfa.2015.12.007</a>
  apa: Nam, P., Napiórkowski, M. M., &#38; Solovej, J. (2016). Diagonalization of
    bosonic quadratic Hamiltonians by Bogoliubov transformations. <i>Journal of Functional
    Analysis</i>. Academic Press. <a href="https://doi.org/10.1016/j.jfa.2015.12.007">https://doi.org/10.1016/j.jfa.2015.12.007</a>
  chicago: Nam, Phan, Marcin M Napiórkowski, and Jan Solovej. “Diagonalization of
    Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” <i>Journal of Functional
    Analysis</i>. Academic Press, 2016. <a href="https://doi.org/10.1016/j.jfa.2015.12.007">https://doi.org/10.1016/j.jfa.2015.12.007</a>.
  ieee: P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic
    Hamiltonians by Bogoliubov transformations,” <i>Journal of Functional Analysis</i>,
    vol. 270, no. 11. Academic Press, pp. 4340–4368, 2016.
  ista: Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic
    Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11),
    4340–4368.
  mla: Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov
    Transformations.” <i>Journal of Functional Analysis</i>, vol. 270, no. 11, Academic
    Press, 2016, pp. 4340–68, doi:<a href="https://doi.org/10.1016/j.jfa.2015.12.007">10.1016/j.jfa.2015.12.007</a>.
  short: P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270
    (2016) 4340–4368.
date_created: 2018-12-11T11:52:38Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2021-01-12T06:51:30Z
day: '01'
department:
- _id: RoSe
doi: 10.1016/j.jfa.2015.12.007
ec_funded: 1
intvolume: '       270'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1508.07321
month: '06'
oa: 1
oa_version: Submitted Version
page: 4340 - 4368
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
- _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: Journal of Functional Analysis
publication_status: published
publisher: Academic Press
publist_id: '5626'
quality_controlled: '1'
scopus_import: 1
status: public
title: Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 270
year: '2016'
...
---
_id: '5813'
abstract:
- lang: eng
  text: We consider homogeneous Bose gas in a large cubic box with periodic boundary
    conditions, at zero temperature. We analyze its excitation spectrum in a certain
    kind of a mean-field infinite-volume limit. We prove that under appropriate conditions
    the excitation spectrum has the form predicted by the Bogoliubov approximation.
    Our result can be viewed as an extension of the result of Seiringer (Commun. Math.
    Phys.306:565–578, 2011) to large volumes.
article_processing_charge: No
author:
- first_name: Jan
  full_name: Dereziński, Jan
  last_name: Dereziński
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
citation:
  ama: Dereziński J, Napiórkowski MM. Excitation spectrum of interacting bosons in
    the Mean-Field Infinite-Volume limit. <i>Annales Henri Poincaré</i>. 2014;15(12):2409-2439.
    doi:<a href="https://doi.org/10.1007/s00023-013-0302-4">10.1007/s00023-013-0302-4</a>
  apa: Dereziński, J., &#38; Napiórkowski, M. M. (2014). Excitation spectrum of interacting
    bosons in the Mean-Field Infinite-Volume limit. <i>Annales Henri Poincaré</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00023-013-0302-4">https://doi.org/10.1007/s00023-013-0302-4</a>
  chicago: Dereziński, Jan, and Marcin M Napiórkowski. “Excitation Spectrum of Interacting
    Bosons in the Mean-Field Infinite-Volume Limit.” <i>Annales Henri Poincaré</i>.
    Springer Nature, 2014. <a href="https://doi.org/10.1007/s00023-013-0302-4">https://doi.org/10.1007/s00023-013-0302-4</a>.
  ieee: J. Dereziński and M. M. Napiórkowski, “Excitation spectrum of interacting
    bosons in the Mean-Field Infinite-Volume limit,” <i>Annales Henri Poincaré</i>,
    vol. 15, no. 12. Springer Nature, pp. 2409–2439, 2014.
  ista: Dereziński J, Napiórkowski MM. 2014. Excitation spectrum of interacting bosons
    in the Mean-Field Infinite-Volume limit. Annales Henri Poincaré. 15(12), 2409–2439.
  mla: Dereziński, Jan, and Marcin M. Napiórkowski. “Excitation Spectrum of Interacting
    Bosons in the Mean-Field Infinite-Volume Limit.” <i>Annales Henri Poincaré</i>,
    vol. 15, no. 12, Springer Nature, 2014, pp. 2409–39, doi:<a href="https://doi.org/10.1007/s00023-013-0302-4">10.1007/s00023-013-0302-4</a>.
  short: J. Dereziński, M.M. Napiórkowski, Annales Henri Poincaré 15 (2014) 2409–2439.
date_created: 2019-01-10T09:02:58Z
date_published: 2014-01-10T00:00:00Z
date_updated: 2021-11-16T08:13:24Z
day: '10'
ddc:
- '530'
doi: 10.1007/s00023-013-0302-4
extern: '1'
file:
- access_level: open_access
  checksum: 1f6c32c5d6ec90cdb0718c7f0103342e
  content_type: application/pdf
  creator: dernst
  date_created: 2019-01-10T09:04:45Z
  date_updated: 2020-07-14T12:47:11Z
  file_id: '5814'
  file_name: 2014_Annales_Derezinski.pdf
  file_size: 865230
  relation: main_file
file_date_updated: 2020-07-14T12:47:11Z
has_accepted_license: '1'
intvolume: '        15'
issue: '12'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 2409-2439
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  link:
  - relation: erratum
    url: https://doi.org/10.1007/s00023-014-0390-9
status: public
title: Excitation spectrum of interacting bosons in the Mean-Field Infinite-Volume
  limit
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 15
year: '2014'
...