---
_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. Letters in Mathematical Physics. 2021;111(2). doi:10.1007/s11005-021-01375-4
apa: Napiórkowski, M. M., & Seiringer, R. (2021). Free energy asymptotics of
the quantum Heisenberg spin chain. Letters in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s11005-021-01375-4
chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics
of the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01375-4.
ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum
Heisenberg spin chain,” Letters in Mathematical Physics, 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.” Letters in Mathematical Physics, vol.
111, no. 2, 31, Springer Nature, 2021, doi:10.1007/s11005-021-01375-4.
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'
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checksum: 687fef1525789c0950de90468dd81604
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creator: dernst
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license: https://creativecommons.org/licenses/by/4.0/
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.).
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. Communications in Mathematical Physics. 2018;360(1):347-403.
doi:10.1007/s00220-017-3064-x'
apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). The Bogoliubov
free energy functional II: The dilute Limit. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-017-3064-x'
chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov
Free Energy Functional II: The Dilute Limit.” Communications in Mathematical
Physics. Springer, 2018. https://doi.org/10.1007/s00220-017-3064-x.'
ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy
functional II: The dilute Limit,” Communications in Mathematical Physics,
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.” Communications in Mathematical Physics, vol. 360, no.
1, Springer, 2018, pp. 347–403, doi:10.1007/s00220-017-3064-x.'
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: '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
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. EPL. 2018;121(1).
doi:10.1209/0295-5075/121/10007
apa: Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). Calculation of
the critical temperature of a dilute Bose gas in the Bogoliubov approximation.
EPL. IOP Publishing Ltd. https://doi.org/10.1209/0295-5075/121/10007
chicago: Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “Calculation of
the Critical Temperature of a Dilute Bose Gas in the Bogoliubov Approximation.”
EPL. IOP Publishing Ltd., 2018. https://doi.org/10.1209/0295-5075/121/10007.
ieee: M. M. Napiórkowski, R. Reuvers, and J. Solovej, “Calculation of the critical
temperature of a dilute Bose gas in the Bogoliubov approximation,” EPL,
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.” EPL, vol. 121, no.
1, 10007, IOP Publishing Ltd., 2018, doi:10.1209/0295-5075/121/10007.
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: '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
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. Archive for Rational Mechanics
and Analysis. 2018;229(3):1037-1090. doi:10.1007/s00205-018-1232-6'
apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. P. (2018). The Bogoliubov
free energy functional I: Existence of minimizers and phase diagram. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-018-1232-6'
chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov
Free Energy Functional I: Existence of Minimizers and Phase Diagram.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2018. https://doi.org/10.1007/s00205-018-1232-6.'
ieee: 'M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy
functional I: Existence of minimizers and phase diagram,” Archive for Rational
Mechanics and Analysis, 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.” Archive for Rational Mechanics
and Analysis, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:10.1007/s00205-018-1232-6.'
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: '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 < 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. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738.
doi:10.4310/ATMP.2017.v21.n3.a4
apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field
dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4
chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field
Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics.
International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4.
ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics
of interacting bosons,” Advances in Theoretical and Mathematical Physics,
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.” Advances in Theoretical and Mathematical Physics,
vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4.
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: '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. Journal de Mathématiques Pures et Appliquées. 2017;108(5):662-688.
doi:10.1016/j.matpur.2017.05.013
apa: Nam, P., & Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov
correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées.
Elsevier. https://doi.org/10.1016/j.matpur.2017.05.013
chicago: Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov
Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées.
Elsevier, 2017. https://doi.org/10.1016/j.matpur.2017.05.013.
ieee: P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction
to mean field dynamics,” Journal de Mathématiques Pures et Appliquées,
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.” Journal de Mathématiques Pures et Appliquées,
vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:10.1016/j.matpur.2017.05.013.
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: '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. Journal of Functional Analysis. 2016;270(11):4340-4368.
doi:10.1016/j.jfa.2015.12.007
apa: Nam, P., Napiórkowski, M. M., & Solovej, J. (2016). Diagonalization of
bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional
Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2015.12.007
chicago: Nam, Phan, Marcin M Napiórkowski, and Jan Solovej. “Diagonalization of
Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional
Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2015.12.007.
ieee: P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic
Hamiltonians by Bogoliubov transformations,” Journal of Functional Analysis,
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.” Journal of Functional Analysis, vol. 270, no. 11, Academic
Press, 2016, pp. 4340–68, doi:10.1016/j.jfa.2015.12.007.
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:
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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'
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status: public
title: Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
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...
---
_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. Annales Henri Poincaré. 2014;15(12):2409-2439.
doi:10.1007/s00023-013-0302-4
apa: Dereziński, J., & Napiórkowski, M. M. (2014). Excitation spectrum of interacting
bosons in the Mean-Field Infinite-Volume limit. Annales Henri Poincaré.
Springer Nature. https://doi.org/10.1007/s00023-013-0302-4
chicago: Dereziński, Jan, and Marcin M Napiórkowski. “Excitation Spectrum of Interacting
Bosons in the Mean-Field Infinite-Volume Limit.” Annales Henri Poincaré.
Springer Nature, 2014. https://doi.org/10.1007/s00023-013-0302-4.
ieee: J. Dereziński and M. M. Napiórkowski, “Excitation spectrum of interacting
bosons in the Mean-Field Infinite-Volume limit,” Annales Henri Poincaré,
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.” Annales Henri Poincaré,
vol. 15, no. 12, Springer Nature, 2014, pp. 2409–39, doi:10.1007/s00023-013-0302-4.
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
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creator: dernst
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date_updated: 2020-07-14T12:47:11Z
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file_name: 2014_Annales_Derezinski.pdf
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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
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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'
...