{"publication":"Pure and Applied Analysis","issue":"4","publication_status":"published","month":"10","date_created":"2024-01-28T23:01:43Z","external_id":{"arxiv":["1912.11004"]},"publisher":"Mathematical Sciences Publishers","article_type":"original","status":"public","_id":"14890","acknowledgement":"We are grateful for the hospitality of Central China Normal University (CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher, Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research\r\nTraining Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk lodowska-Curie Grant Agreement No. 754411.","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-02-05T09:26:31Z","type":"journal_article","oa_version":"Preprint","doi":"10.2140/paa.2021.3.677","department":[{"_id":"RoSe"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"day":"01","author":[{"full_name":"Bossmann, Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","last_name":"Bossmann","orcid":"0000-0002-6854-1343"},{"full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889"},{"full_name":"Pickl, Peter","first_name":"Peter","last_name":"Pickl"},{"full_name":"Soffer, Avy","first_name":"Avy","last_name":"Soffer"}],"page":"677-726","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.11004","open_access":"1"}],"year":"2021","abstract":[{"lang":"eng","text":"We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions."}],"oa":1,"quality_controlled":"1","date_published":"2021-10-01T00:00:00Z","volume":3,"scopus_import":"1","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"article_processing_charge":"No","citation":{"ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726.","mla":"Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>.","apa":"Bossmann, L., Petrat, S. P., Pickl, P., &#38; Soffer, A. (2021). Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>","ama":"Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. 2021;3(4):677-726. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>","chicago":"Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>.","short":"L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726.","ieee":"L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021."},"intvolume":"         3","title":"Beyond Bogoliubov dynamics"}