[{"type":"journal_article","publication_status":"published","quality_controlled":"1","doi":"10.1007/s11005-021-01375-4","publisher":"Springer Nature","oa":1,"pmid":1,"article_processing_charge":"Yes (via OA deal)","date_published":"2021-03-09T00:00:00Z","citation":{"short":"M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).","ista":"Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.","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.","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>","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>."},"article_type":"original","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2021-03-22T11:01:09Z","_id":"9256","issue":"2","author":[{"full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer"}],"date_created":"2021-03-21T23:01:19Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","isi":1,"file":[{"date_updated":"2021-03-22T11:01:09Z","access_level":"open_access","relation":"main_file","file_id":"9273","date_created":"2021-03-22T11:01:09Z","creator":"dernst","content_type":"application/pdf","file_size":397962,"checksum":"687fef1525789c0950de90468dd81604","success":1,"file_name":"2021_LettersMathPhysics_Napiorkowski.pdf"}],"title":"Free energy asymptotics of the quantum Heisenberg spin chain","ddc":["510"],"article_number":"31","intvolume":"       111","external_id":{"pmid":["33785980"],"isi":["000626837400001"]},"department":[{"_id":"RoSe"}],"has_accepted_license":"1","oa_version":"Published Version","publication":"Letters in Mathematical Physics","scopus_import":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"day":"09","license":"https://creativecommons.org/licenses/by/4.0/","year":"2021","date_updated":"2026-04-02T14:06:48Z","volume":111,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"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).","status":"public","month":"03"},{"doi":"10.1007/s00220-017-3064-x","oa":1,"publisher":"Springer","quality_controlled":"1","type":"journal_article","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1511.05953","open_access":"1"}],"abstract":[{"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.).","lang":"eng"}],"_id":"554","date_published":"2018-05-01T00:00:00Z","article_processing_charge":"No","citation":{"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.","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403.","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>.","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>","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.","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>.","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>"},"title":"The Bogoliubov free energy functional II: The dilute Limit","project":[{"call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"date_created":"2018-12-11T11:47:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","author":[{"first_name":"Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M"},{"full_name":"Reuvers, Robin","first_name":"Robin","last_name":"Reuvers"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"department":[{"_id":"RoSe"}],"intvolume":"       360","external_id":{"arxiv":["1511.05953"]},"language":[{"iso":"eng"}],"publist_id":"7260","scopus_import":"1","oa_version":"Submitted Version","publication":"Communications in Mathematical Physics","year":"2018","publication_identifier":{"issn":["0010-3616"]},"day":"01","volume":360,"date_updated":"2025-07-10T11:52:52Z","month":"05","status":"public","page":"347-403","arxiv":1},{"year":"2018","day":"01","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"language":[{"iso":"eng"}],"oa_version":"Preprint","publication":"Archive for Rational Mechanics and Analysis","scopus_import":"1","status":"public","month":"09","arxiv":1,"page":"1037-1090","date_updated":"2025-04-15T08:26:15Z","volume":229,"_id":"6002","abstract":[{"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.","lang":"eng"}],"citation":{"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.","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>.","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>","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.","short":"M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090.","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>."},"article_processing_charge":"No","date_published":"2018-09-01T00:00:00Z","quality_controlled":"1","doi":"10.1007/s00205-018-1232-6","oa":1,"publisher":"Springer Nature","main_file_link":[{"url":"https://arxiv.org/abs/1511.05935","open_access":"1"}],"publication_status":"published","type":"journal_article","department":[{"_id":"RoSe"}],"intvolume":"       229","external_id":{"isi":["000435367300003"],"arxiv":["1511.05935"]},"isi":1,"title":"The Bogoliubov free energy functional I: Existence of minimizers and phase diagram","author":[{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","first_name":"Marcin M"},{"last_name":"Reuvers","first_name":"Robin","full_name":"Reuvers, Robin"},{"full_name":"Solovej, Jan Philip","last_name":"Solovej","first_name":"Jan Philip"}],"issue":"3","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"}],"date_created":"2019-02-14T13:40:53Z"},{"volume":121,"date_updated":"2025-04-15T08:26:14Z","month":"01","status":"public","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).","arxiv":1,"language":[{"iso":"eng"}],"publist_id":"7432","scopus_import":"1","oa_version":"Preprint","publication":"EPL","year":"2018","day":"01","title":"Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation","isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:46:15Z","project":[{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"}],"author":[{"full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M"},{"first_name":"Robin","last_name":"Reuvers","full_name":"Reuvers, Robin"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan"}],"issue":"1","department":[{"_id":"RoSe"}],"intvolume":"       121","external_id":{"arxiv":["1706.01822"],"isi":["000460003000003"]},"article_number":"10007","publisher":"IOP Publishing","oa":1,"doi":"10.1209/0295-5075/121/10007","quality_controlled":"1","publication_status":"published","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1706.01822","open_access":"1"}],"_id":"399","abstract":[{"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.","lang":"eng"}],"article_type":"original","citation":{"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, 2018.","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, 2018, doi:<a href=\"https://doi.org/10.1209/0295-5075/121/10007\">10.1209/0295-5075/121/10007</a>.","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>","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.","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, EPL 121 (2018).","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, 2018. <a href=\"https://doi.org/10.1209/0295-5075/121/10007\">https://doi.org/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. <a href=\"https://doi.org/10.1209/0295-5075/121/10007\">https://doi.org/10.1209/0295-5075/121/10007</a>"},"date_published":"2018-01-01T00:00:00Z","article_processing_charge":"No"},{"year":"2017","day":"01","publication_identifier":{"issn":["0021-7824"]},"publist_id":"6928","language":[{"iso":"eng"}],"corr_author":"1","publication":"Journal de Mathématiques Pures et Appliquées","oa_version":"Submitted Version","scopus_import":"1","status":"public","month":"11","arxiv":1,"page":"662 - 688","date_updated":"2025-06-04T09:41:48Z","volume":108,"_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."}],"citation":{"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>.","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.","short":"P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108 (2017) 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>.","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>","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."},"article_processing_charge":"No","date_published":"2017-11-01T00:00:00Z","quality_controlled":"1","publisher":"Elsevier","oa":1,"doi":"10.1016/j.matpur.2017.05.013","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.05240"}],"type":"journal_article","publication_status":"published","department":[{"_id":"RoSe"}],"intvolume":"       108","external_id":{"arxiv":["1604.05240"],"isi":["000414113600003"]},"isi":1,"title":"A note on the validity of Bogoliubov correction to mean field dynamics","author":[{"last_name":"Nam","first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Nam, Phan"},{"full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","first_name":"Marcin M"}],"issue":"5","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:48:15Z","project":[{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}]},{"das_tickbox":"1","volume":21,"date_updated":"2026-07-06T13:34:16Z","arxiv":1,"page":"683 - 738","status":"public","month":"01","oa_version":"Submitted Version","publication":"Advances in Theoretical and Mathematical Physics","scopus_import":"1","publist_id":"7336","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1095-0761"]},"day":"01","year":"2017","issue":"3","author":[{"last_name":"Nam","first_name":"Phan","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","first_name":"Marcin M"}],"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"}],"date_created":"2018-12-11T11:46:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"title":"Bogoliubov correction to the mean-field dynamics of interacting bosons","external_id":{"arxiv":["1509.04631"],"isi":["000409382300004"]},"intvolume":"        21","department":[{"_id":"RoSe"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.04631"}],"publication_status":"published","type":"journal_article","quality_controlled":"1","oa":1,"publisher":"International Press of Boston","doi":"10.4310/ATMP.2017.v21.n3.a4","ec_funded":1,"date_published":"2017-01-01T00:00:00Z","article_processing_charge":"No","citation":{"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 of Boston, pp. 683–738, 2017.","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 of Boston, 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>.","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>","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.","short":"P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics 21 (2017) 683–738.","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 of Boston, 2017. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/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 of Boston. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>"},"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."}],"_id":"484"},{"scopus_import":"1","publication":"Journal of Functional Analysis","oa_version":"Submitted Version","corr_author":"1","language":[{"iso":"eng"}],"publist_id":"5626","day":"01","year":"2016","volume":270,"date_updated":"2025-09-18T11:04:09Z","page":"4340 - 4368","arxiv":1,"month":"06","status":"public","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.).","type":"journal_article","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/1508.07321","open_access":"1"}],"oa":1,"publisher":"Academic Press","doi":"10.1016/j.jfa.2015.12.007","quality_controlled":"1","citation":{"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.","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>.","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>","ista":"Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11), 4340–4368.","short":"P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368.","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>.","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>"},"date_published":"2016-06-01T00:00:00Z","article_processing_charge":"No","ec_funded":1,"_id":"1545","abstract":[{"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.","lang":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:52:38Z","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","last_name":"Nam"},{"full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M","last_name":"Napiórkowski"},{"full_name":"Solovej, Jan","first_name":"Jan","last_name":"Solovej"}],"issue":"11","title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations","isi":1,"intvolume":"       270","external_id":{"isi":["000375241700011"],"arxiv":["1508.07321"]},"department":[{"_id":"RoSe"}]},{"publication_identifier":{"issn":["1424-0637","1424-0661"]},"day":"10","year":"2014","publication":"Annales Henri Poincaré","oa_version":"Published Version","language":[{"iso":"eng"}],"page":"2409-2439","extern":"1","month":"01","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_updated":"2021-11-16T08:13:24Z","volume":15,"article_processing_charge":"No","date_published":"2014-01-10T00:00:00Z","citation":{"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.","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>.","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>","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.","short":"J. Dereziński, M.M. Napiórkowski, Annales Henri Poincaré 15 (2014) 2409–2439.","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>."},"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."}],"file_date_updated":"2020-07-14T12:47:11Z","_id":"5813","type":"journal_article","publication_status":"published","oa":1,"publisher":"Springer Nature","doi":"10.1007/s00023-013-0302-4","quality_controlled":"1","intvolume":"        15","ddc":["530"],"has_accepted_license":"1","date_created":"2019-01-10T09:02:58Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","issue":"12","author":[{"last_name":"Dereziński","first_name":"Jan","full_name":"Dereziński, Jan"},{"first_name":"Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M"}],"title":"Excitation spectrum of interacting bosons in the Mean-Field Infinite-Volume limit","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s00023-014-0390-9"}]},"file":[{"creator":"dernst","file_size":865230,"content_type":"application/pdf","checksum":"1f6c32c5d6ec90cdb0718c7f0103342e","file_name":"2014_Annales_Derezinski.pdf","date_updated":"2020-07-14T12:47:11Z","access_level":"open_access","relation":"main_file","date_created":"2019-01-10T09:04:45Z","file_id":"5814"}]}]