--- _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' 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 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: - 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. 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 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' ...