[{"year":"2021","isi":1,"has_accepted_license":"1","publication":"Letters in Mathematical Physics","day":"09","date_created":"2021-03-21T23:01:19Z","date_published":"2021-03-09T00:00:00Z","doi":"10.1007/s11005-021-01375-4","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).","oa":1,"quality_controlled":"1","publisher":"Springer Nature","citation":{"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","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","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.","short":"M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).","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.","ista":"Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000626837400001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"title":"Free energy asymptotics of the quantum Heisenberg spin chain","article_number":"31","publication_status":"published","publication_identifier":{"issn":["03779017"],"eissn":["15730530"]},"language":[{"iso":"eng"}],"file":[{"file_size":397962,"date_updated":"2021-03-22T11:01:09Z","creator":"dernst","file_name":"2021_LettersMathPhysics_Napiorkowski.pdf","date_created":"2021-03-22T11:01:09Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"687fef1525789c0950de90468dd81604","file_id":"9273"}],"volume":111,"issue":"2","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."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 111","month":"03","date_updated":"2023-08-07T14:17:00Z","ddc":["510"],"file_date_updated":"2021-03-22T11:01:09Z","department":[{"_id":"RoSe"}],"_id":"9256","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public"},{"project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"citation":{"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.","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.","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","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.","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"7260","author":[{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"},{"first_name":"Robin","last_name":"Reuvers","full_name":"Reuvers, Robin"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"external_id":{"arxiv":["1511.05953"]},"title":"The Bogoliubov free energy functional II: The dilute Limit","quality_controlled":"1","publisher":"Springer","oa":1,"year":"2018","day":"01","publication":"Communications in Mathematical Physics","page":"347-403","doi":"10.1007/s00220-017-3064-x","date_published":"2018-05-01T00:00:00Z","date_created":"2018-12-11T11:47:09Z","_id":"554","type":"journal_article","status":"public","date_updated":"2021-01-12T08:02:35Z","department":[{"_id":"RoSe"}],"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.)."}],"oa_version":"Submitted Version","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.05953"}],"month":"05","intvolume":" 360","publication_identifier":{"issn":["00103616"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":360},{"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"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1706.01822","open_access":"1"}],"scopus_import":"1","intvolume":" 121","month":"01","publication_status":"published","language":[{"iso":"eng"}],"volume":121,"issue":"1","_id":"399","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-09-08T13:30:51Z","department":[{"_id":"RoSe"}],"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).","oa":1,"quality_controlled":"1","publisher":"IOP Publishing Ltd.","year":"2018","isi":1,"publication":"EPL","day":"01","date_created":"2018-12-11T11:46:15Z","doi":"10.1209/0295-5075/121/10007","date_published":"2018-01-01T00:00:00Z","article_number":"10007","project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"citation":{"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.","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.","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","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.","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, EPL 121 (2018).","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000460003000003"],"arxiv":["1706.01822"]},"author":[{"last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M","first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Robin","last_name":"Reuvers","full_name":"Reuvers, Robin"},{"last_name":"Solovej","full_name":"Solovej, Jan","first_name":"Jan"}],"publist_id":"7432","title":"Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation"},{"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"publication_status":"published","volume":229,"issue":"3","oa_version":"Preprint","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."}],"month":"09","intvolume":" 229","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1511.05935","open_access":"1"}],"date_updated":"2023-09-19T14:33:12Z","department":[{"_id":"RoSe"}],"_id":"6002","status":"public","type":"journal_article","day":"01","publication":"Archive for Rational Mechanics and Analysis","isi":1,"year":"2018","doi":"10.1007/s00205-018-1232-6","date_published":"2018-09-01T00:00:00Z","date_created":"2019-02-14T13:40:53Z","page":"1037-1090","publisher":"Springer Nature","quality_controlled":"1","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","short":"M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090.","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. 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Springer Nature, 2018. https://doi.org/10.1007/s00205-018-1232-6."},"title":"The Bogoliubov free energy functional I: Existence of minimizers and phase diagram","author":[{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski"},{"last_name":"Reuvers","full_name":"Reuvers, Robin","first_name":"Robin"},{"full_name":"Solovej, Jan Philip","last_name":"Solovej","first_name":"Jan Philip"}],"external_id":{"arxiv":["1511.05935"],"isi":["000435367300003"]},"article_processing_charge":"No","project":[{"call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}]},{"type":"journal_article","status":"public","_id":"484","department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T08:00:58Z","main_file_link":[{"url":"https://arxiv.org/abs/1509.04631","open_access":"1"}],"scopus_import":1,"intvolume":" 21","month":"01","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."}],"oa_version":"Submitted Version","ec_funded":1,"issue":"3","volume":21,"publication_status":"published","publication_identifier":{"issn":["10950761"]},"language":[{"iso":"eng"}],"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"publist_id":"7336","author":[{"last_name":"Nam","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"},{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87"}],"title":"Bogoliubov correction to the mean-field dynamics of interacting bosons","citation":{"short":"P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics 21 (2017) 683–738.","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.","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","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","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.","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.","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."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"International Press","quality_controlled":"1","page":"683 - 738","date_created":"2018-12-11T11:46:43Z","doi":"10.4310/ATMP.2017.v21.n3.a4","date_published":"2017-01-01T00:00:00Z","year":"2017","publication":"Advances in Theoretical and Mathematical Physics","day":"01"},{"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."}],"oa_version":"Submitted Version","main_file_link":[{"url":"https://arxiv.org/abs/1604.05240","open_access":"1"}],"scopus_import":"1","intvolume":" 108","month":"11","publication_status":"published","publication_identifier":{"issn":["00217824"]},"language":[{"iso":"eng"}],"volume":108,"issue":"5","_id":"739","type":"journal_article","status":"public","date_updated":"2023-09-27T12:52:07Z","department":[{"_id":"RoSe"}],"oa":1,"quality_controlled":"1","publisher":"Elsevier","year":"2017","isi":1,"publication":"Journal de Mathématiques Pures et Appliquées","day":"01","page":"662 - 688","date_created":"2018-12-11T11:48:15Z","doi":"10.1016/j.matpur.2017.05.013","date_published":"2017-11-01T00:00:00Z","project":[{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"}],"citation":{"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.","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.","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.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000414113600003"]},"article_processing_charge":"No","author":[{"first_name":"Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","last_name":"Nam","full_name":"Nam, Phan"},{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6928","title":"A note on the validity of Bogoliubov correction to mean field dynamics"},{"date_created":"2018-12-11T11:52:38Z","date_published":"2016-06-01T00:00:00Z","doi":"10.1016/j.jfa.2015.12.007","page":"4340 - 4368","publication":"Journal of Functional Analysis","day":"01","year":"2016","oa":1,"quality_controlled":"1","publisher":"Academic Press","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.).","title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations","publist_id":"5626","author":[{"last_name":"Nam","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan"},{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"},{"first_name":"Jan","full_name":"Solovej, Jan","last_name":"Solovej"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","short":"P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368."},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"volume":270,"issue":"11","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 270","month":"06","main_file_link":[{"url":"http://arxiv.org/abs/1508.07321","open_access":"1"}],"scopus_import":1,"oa_version":"Submitted Version","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."}],"department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T06:51:30Z","status":"public","type":"journal_article","_id":"1545"},{"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2020-07-14T12:47:11Z","file_size":865230,"date_created":"2019-01-10T09:04:45Z","file_name":"2014_Annales_Derezinski.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"5814","checksum":"1f6c32c5d6ec90cdb0718c7f0103342e"}],"publication_status":"published","publication_identifier":{"issn":["1424-0637","1424-0661"]},"issue":"12","volume":15,"related_material":{"link":[{"url":"https://doi.org/10.1007/s00023-014-0390-9","relation":"erratum"}]},"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"intvolume":" 15","month":"01","ddc":["530"],"extern":"1","date_updated":"2021-11-16T08:13:24Z","file_date_updated":"2020-07-14T12:47:11Z","_id":"5813","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","publication":"Annales Henri Poincaré","day":"10","year":"2014","has_accepted_license":"1","date_created":"2019-01-10T09:02:58Z","doi":"10.1007/s00023-013-0302-4","date_published":"2014-01-10T00:00:00Z","page":"2409-2439","oa":1,"publisher":"Springer Nature","quality_controlled":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"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.","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.","short":"J. Dereziński, M.M. Napiórkowski, Annales Henri Poincaré 15 (2014) 2409–2439.","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.","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","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","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."},"title":"Excitation spectrum of interacting bosons in the Mean-Field Infinite-Volume limit","article_processing_charge":"No","author":[{"first_name":"Jan","last_name":"Dereziński","full_name":"Dereziński, Jan"},{"full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"}]}]