{"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.).","quality_controlled":"1","day":"01","citation":{"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>","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.","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>","short":"P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368.","ista":"Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11), 4340–4368.","mla":"Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” <i>Journal of Functional Analysis</i>, vol. 270, no. 11, Academic Press, 2016, pp. 4340–68, doi:<a href=\"https://doi.org/10.1016/j.jfa.2015.12.007\">10.1016/j.jfa.2015.12.007</a>.","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>."},"department":[{"_id":"RoSe"}],"date_updated":"2021-01-12T06:51:30Z","doi":"10.1016/j.jfa.2015.12.007","volume":270,"oa":1,"ec_funded":1,"publist_id":"5626","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1508.07321","open_access":"1"}],"_id":"1545","year":"2016","author":[{"first_name":"Phan","last_name":"Nam","full_name":"Nam, Phan","id":"404092F4-F248-11E8-B48F-1D18A9856A87"},{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M","first_name":"Marcin M"},{"first_name":"Jan","full_name":"Solovej, Jan","last_name":"Solovej"}],"publication":"Journal of Functional Analysis","issue":"11","title":"Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations","month":"06","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:52:38Z","oa_version":"Submitted Version","date_published":"2016-06-01T00:00:00Z","publisher":"Academic Press","type":"journal_article","page":"4340 - 4368","publication_status":"published","status":"public","intvolume":"       270","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"}]}