{"date_published":"2023-02-21T00:00:00Z","publication_status":"published","date_created":"2024-05-29T06:12:54Z","status":"public","publisher":"Mathematical Sciences Publishers","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-07-31T11:51:43Z","year":"2023","abstract":[{"lang":"eng","text":"We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states ΨN, i.e. states satisfying ⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers."}],"month":"02","doi":"10.2140/pmp.2022.3.939","scopus_import":"1","type":"journal_article","citation":{"ista":"Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.","ieee":"M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases,” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 939–1000, 2023.","mla":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>.","short":"M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.","apa":"Brooks, M., &#38; Seiringer, R. (2023). Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>","chicago":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>.","ama":"Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. 2023;3(4):939-1000. doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>"},"author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","full_name":"Brooks, Morris","first_name":"Morris","orcid":"0000-0002-6249-0928"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"_id":"17074","volume":3,"article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2111.13864"}],"language":[{"iso":"eng"}],"page":"939-1000","day":"21","corr_author":"1","article_processing_charge":"No","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"quality_controlled":"1","acknowledgement":"We are grateful to Rupert Frank for helpful discussions at an early stage of this project.\r\nFunding from the European Union’s Horizon 2020 research and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged.","title":"Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases","oa":1,"department":[{"_id":"RoSe"}],"external_id":{"arxiv":["2111.13864"]},"ec_funded":1,"issue":"4","intvolume":"         3","publication":"Probability and Mathematical Physics"}