[{"publication_identifier":{"eisbn":["9783031454349"],"isbn":["9783031454332"],"issn":["0168-1222"],"eissn":["2365-6425"]},"arxiv":1,"editor":[{"last_name":"Bassi","full_name":"Bassi, Angelo","first_name":"Angelo"},{"full_name":"Goldstein, Sheldon","last_name":"Goldstein","first_name":"Sheldon"},{"first_name":"Roderich","last_name":"Tumulka","full_name":"Tumulka, Roderich"},{"last_name":"Zanghi","full_name":"Zanghi, Nino","first_name":"Nino"}],"publication_status":"published","title":"Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications","date_updated":"2025-01-29T10:35:10Z","external_id":{"arxiv":["2304.12910"]},"date_published":"2024-02-04T00:00:00Z","quality_controlled":"1","abstract":[{"text":"We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an Edgeworth expansion for fluctuations of one-body operators and the computation of the binding energy of an inhomogeneous Bose gas to any order. Finally, we collect related results for the dynamics of the weakly interacting Bose gas and for the regularized Nelson model.","lang":"eng"}],"alternative_title":["Fundamental Theories of Physics"],"series_title":"FTPH","OA_place":"repository","acknowledgement":"It is our pleasure to thank Marco Falconi, Nataša Pavlović, Peter Pickl, Robert Seiringer and Avy Soffer for the collaboration on the works [11, 13, 14, 21, 33, 39]. L.B. was supported by the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111). N.L. acknowledges support from the Swiss National Science Foundation through the NCCR SwissMap and funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101024712. S.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 512258249.","type":"book_chapter","citation":{"short":"L. Bossmann, N. Leopold, D.J. Mitrouskas, S. Petrat, in:, A. Bassi, S. Goldstein, R. Tumulka, N. Zanghi (Eds.), Physics and the Nature of Reality, Springer Nature, Cham, 2024, pp. 307–321.","chicago":"Bossmann, Lea, Nikolai Leopold, David Johannes Mitrouskas, and Sören Petrat. “Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications.” In <i>Physics and the Nature of Reality</i>, edited by Angelo Bassi, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghi, 215:307–21. FTPH. Cham: Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-45434-9_22\">https://doi.org/10.1007/978-3-031-45434-9_22</a>.","apa":"Bossmann, L., Leopold, N., Mitrouskas, D. J., &#38; Petrat, S. (2024). Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications. In A. Bassi, S. Goldstein, R. Tumulka, &#38; N. Zanghi (Eds.), <i>Physics and the Nature of Reality</i> (Vol. 215, pp. 307–321). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-45434-9_22\">https://doi.org/10.1007/978-3-031-45434-9_22</a>","mla":"Bossmann, Lea, et al. “Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications.” <i>Physics and the Nature of Reality</i>, edited by Angelo Bassi et al., vol. 215, Springer Nature, 2024, pp. 307–21, doi:<a href=\"https://doi.org/10.1007/978-3-031-45434-9_22\">10.1007/978-3-031-45434-9_22</a>.","ista":"Bossmann L, Leopold N, Mitrouskas DJ, Petrat S. 2024.Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications. In: Physics and the Nature of Reality. Fundamental Theories of Physics, vol. 215, 307–321.","ieee":"L. Bossmann, N. Leopold, D. J. Mitrouskas, and S. Petrat, “Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications,” in <i>Physics and the Nature of Reality</i>, vol. 215, A. Bassi, S. Goldstein, R. Tumulka, and N. Zanghi, Eds. Cham: Springer Nature, 2024, pp. 307–321.","ama":"Bossmann L, Leopold N, Mitrouskas DJ, Petrat S. Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications. In: Bassi A, Goldstein S, Tumulka R, Zanghi N, eds. <i>Physics and the Nature of Reality</i>. Vol 215. FTPH. Cham: Springer Nature; 2024:307-321. doi:<a href=\"https://doi.org/10.1007/978-3-031-45434-9_22\">10.1007/978-3-031-45434-9_22</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Physics and the Nature of Reality","oa":1,"month":"02","_id":"18948","status":"public","oa_version":"Preprint","doi":"10.1007/978-3-031-45434-9_22","scopus_import":"1","intvolume":"       215","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","full_name":"Bossmann, Lea","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"first_name":"Nikolai","full_name":"Leopold, Nikolai","last_name":"Leopold"},{"full_name":"Mitrouskas, David Johannes","last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes"},{"first_name":"Sören","full_name":"Petrat, Sören","last_name":"Petrat"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2304.12910"}],"volume":215,"date_created":"2025-01-29T10:30:08Z","place":"Cham","publisher":"Springer Nature","day":"04","article_processing_charge":"No","department":[{"_id":"RoSe"}],"OA_type":"green","year":"2024","language":[{"iso":"eng"}],"page":"307-321"},{"article_number":"48","_id":"15318","ddc":["510"],"file_date_updated":"2024-04-16T11:09:37Z","oa_version":"Published Version","status":"public","month":"04","oa":1,"volume":191,"date_created":"2024-04-14T22:01:02Z","author":[{"full_name":"Bossmann, Lea","last_name":"Bossmann","orcid":"0000-0002-6854-1343","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea"},{"first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","last_name":"Leopold"},{"full_name":"Mitrouskas, David Johannes","last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"orcid":"0000-0002-9166-5889","last_name":"Petrat","full_name":"Petrat, Sören P","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"       191","doi":"10.1007/s10955-024-03260-5","scopus_import":"1","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","issue":"4","day":"06","publisher":"Springer Nature","article_type":"original","year":"2024","language":[{"iso":"eng"}],"arxiv":1,"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"quality_controlled":"1","abstract":[{"text":"We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.","lang":"eng"}],"isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"date_published":"2024-04-06T00:00:00Z","external_id":{"isi":["001197663100002"],"arxiv":["2307.13115"]},"title":"A note on the binding energy for Bosons in the mean-field limit","publication_status":"published","date_updated":"2025-09-04T13:36:49Z","type":"journal_article","acknowledgement":"It is a pleasure to thank Phan Thành Nam for helpful discussions on bosonic atoms. L.B. was supported by the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111). N.L. gratefully acknowledges support from the Swiss National Science Foundation through the NCCR SwissMap and funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant agreement No 101024712. S.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project number 512258249.\r\nOpen Access funding enabled and organized by Projekt DEAL.","file":[{"file_name":"2024_JourStatPhysics_Bossmann.pdf","date_created":"2024-04-16T11:09:37Z","creator":"dernst","access_level":"open_access","success":1,"date_updated":"2024-04-16T11:09:37Z","file_id":"15325","file_size":398665,"checksum":"839242a9ec1c01158112de25f196e60d","relation":"main_file","content_type":"application/pdf"}],"publication":"Journal of Statistical Physics","citation":{"mla":"Bossmann, Lea, et al. “A Note on the Binding Energy for Bosons in the Mean-Field Limit.” <i>Journal of Statistical Physics</i>, vol. 191, no. 4, 48, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s10955-024-03260-5\">10.1007/s10955-024-03260-5</a>.","ista":"Bossmann L, Leopold NK, Mitrouskas DJ, Petrat SP. 2024. A note on the binding energy for Bosons in the mean-field limit. Journal of Statistical Physics. 191(4), 48.","ieee":"L. Bossmann, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “A note on the binding energy for Bosons in the mean-field limit,” <i>Journal of Statistical Physics</i>, vol. 191, no. 4. Springer Nature, 2024.","ama":"Bossmann L, Leopold NK, Mitrouskas DJ, Petrat SP. A note on the binding energy for Bosons in the mean-field limit. <i>Journal of Statistical Physics</i>. 2024;191(4). doi:<a href=\"https://doi.org/10.1007/s10955-024-03260-5\">10.1007/s10955-024-03260-5</a>","short":"L. Bossmann, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Journal of Statistical Physics 191 (2024).","chicago":"Bossmann, Lea, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “A Note on the Binding Energy for Bosons in the Mean-Field Limit.” <i>Journal of Statistical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10955-024-03260-5\">https://doi.org/10.1007/s10955-024-03260-5</a>.","apa":"Bossmann, L., Leopold, N. K., Mitrouskas, D. J., &#38; Petrat, S. P. (2024). A note on the binding energy for Bosons in the mean-field limit. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-024-03260-5\">https://doi.org/10.1007/s10955-024-03260-5</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"department":[{"_id":"RoSe"}],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"03","issue":"4","publisher":"Springer Nature","article_type":"original","language":[{"iso":"eng"}],"year":"2023","OA_type":"hybrid","article_number":"77","oa_version":"Published Version","status":"public","file_date_updated":"2025-06-25T06:20:02Z","_id":"13226","ddc":["510"],"month":"07","oa":1,"date_created":"2023-07-16T22:01:08Z","volume":113,"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","full_name":"Bossmann, Lea","last_name":"Bossmann","orcid":"0000-0002-6854-1343"},{"first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","last_name":"Petrat","full_name":"Petrat, Sören P"}],"intvolume":"       113","scopus_import":"1","doi":"10.1007/s11005-023-01698-4","type":"journal_article","acknowledgement":"It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee for many constructive comments. L.B. gratefully acknowledges funding from the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen Access funding enabled and organized by Projekt DEAL.","OA_place":"publisher","file":[{"file_id":"19898","file_size":586698,"relation":"main_file","content_type":"application/pdf","checksum":"995c902a989a6769fd3db456cfd41111","file_name":"2023_LettersMathPhysics_Bossmann.pdf","date_created":"2025-06-25T06:20:02Z","success":1,"date_updated":"2025-06-25T06:20:02Z","creator":"dernst","access_level":"open_access"}],"publication":"Letters in Mathematical Physics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field Bose gas,” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4. Springer Nature, 2023.","ama":"Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas. <i>Letters in Mathematical Physics</i>. 2023;113(4). doi:<a href=\"https://doi.org/10.1007/s11005-023-01698-4\">10.1007/s11005-023-01698-4</a>","mla":"Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4, 77, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s11005-023-01698-4\">10.1007/s11005-023-01698-4</a>.","ista":"Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77.","chicago":"Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11005-023-01698-4\">https://doi.org/10.1007/s11005-023-01698-4</a>.","apa":"Bossmann, L., &#38; Petrat, S. P. (2023). Weak Edgeworth expansion for the mean-field Bose gas. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-023-01698-4\">https://doi.org/10.1007/s11005-023-01698-4</a>","short":"L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023)."},"ec_funded":1,"arxiv":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"corr_author":"1","abstract":[{"text":"We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion.","lang":"eng"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["001022878900002"],"arxiv":["2208.00199"]},"date_published":"2023-07-03T00:00:00Z","isi":1,"date_updated":"2025-06-25T06:20:15Z","publication_status":"published","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"Weak Edgeworth expansion for the mean-field Bose gas"},{"arxiv":1,"ec_funded":1,"corr_author":"1","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"abstract":[{"lang":"eng","text":"We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix."}],"quality_controlled":"1","external_id":{"arxiv":["2203.00730"],"isi":["000809648100002"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"date_published":"2022-06-10T00:00:00Z","isi":1,"publication_status":"published","title":"Low-energy spectrum and dynamics of the weakly interacting Bose gas","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"date_updated":"2025-04-14T07:43:58Z","type":"journal_article","acknowledgement":"The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged.","file":[{"success":1,"date_updated":"2022-08-11T07:03:02Z","creator":"dernst","access_level":"open_access","file_name":"2022_JourMathPhysics_Bossmann.pdf","date_created":"2022-08-11T07:03:02Z","relation":"main_file","content_type":"application/pdf","checksum":"d0d32c338c1896680174be88c70968fa","file_id":"11784","file_size":5957888}],"publication":"Journal of Mathematical Physics","citation":{"ista":"Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102.","mla":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0089983\">10.1063/5.0089983</a>.","ieee":"L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6. AIP Publishing, 2022.","ama":"Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. 2022;63(6). doi:<a href=\"https://doi.org/10.1063/5.0089983\">10.1063/5.0089983</a>","short":"L. Bossmann, Journal of Mathematical Physics 63 (2022).","chicago":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0089983\">https://doi.org/10.1063/5.0089983</a>.","apa":"Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0089983\">https://doi.org/10.1063/5.0089983</a>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"061102","_id":"11783","file_date_updated":"2022-08-11T07:03:02Z","ddc":["530"],"status":"public","oa_version":"Published Version","month":"06","oa":1,"volume":63,"date_created":"2022-08-11T06:37:52Z","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","last_name":"Bossmann","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343"}],"intvolume":"        63","doi":"10.1063/5.0089983","scopus_import":"1","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"10","issue":"6","publisher":"AIP Publishing","article_type":"original","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"year":"2022","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"year":"2021","page":"677-726","publisher":"Mathematical Sciences Publishers","article_type":"original","day":"01","issue":"4","article_processing_charge":"No","department":[{"_id":"RoSe"}],"scopus_import":"1","doi":"10.2140/paa.2021.3.677","intvolume":"         3","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.11004"}],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","full_name":"Bossmann, Lea","last_name":"Bossmann","orcid":"0000-0002-6854-1343"},{"first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","last_name":"Petrat","full_name":"Petrat, Sören P"},{"first_name":"Peter","last_name":"Pickl","full_name":"Pickl, Peter"},{"first_name":"Avy","full_name":"Soffer, Avy","last_name":"Soffer"}],"date_created":"2024-01-28T23:01:43Z","volume":3,"oa":1,"month":"10","oa_version":"Preprint","status":"public","_id":"14890","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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>","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.","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>","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>.","ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726."},"publication":"Pure and Applied Analysis","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.","type":"journal_article","date_updated":"2025-04-14T07:44:02Z","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"title":"Beyond Bogoliubov dynamics","publication_status":"published","date_published":"2021-10-01T00:00:00Z","external_id":{"arxiv":["1912.11004"]},"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."}],"quality_controlled":"1","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"corr_author":"1","ec_funded":1,"arxiv":1},{"file_date_updated":"2021-04-12T07:15:58Z","_id":"9318","ddc":["510"],"oa_version":"Published Version","status":"public","article_number":"e28","oa":1,"month":"03","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","full_name":"Bossmann, Lea","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"full_name":"Petrat, Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"volume":9,"date_created":"2021-04-11T22:01:15Z","doi":"10.1017/fms.2021.22","scopus_import":"1","intvolume":"         9","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","department":[{"_id":"RoSe"}],"article_type":"original","publisher":"Cambridge University Press","day":"26","year":"2021","language":[{"iso":"eng"}],"ec_funded":1,"publication_identifier":{"eissn":["2050-5094"]},"abstract":[{"text":"We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.","lang":"eng"}],"quality_controlled":"1","title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","publication_status":"published","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"date_updated":"2026-04-02T14:02:29Z","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"date_published":"2021-03-26T00:00:00Z","external_id":{"isi":["000634006900001"]},"acknowledgement":"The first author gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 754411. The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).","type":"journal_article","file":[{"access_level":"open_access","creator":"dernst","date_updated":"2021-04-12T07:15:58Z","success":1,"file_name":"2021_ForumMath_Bossmann.pdf","date_created":"2021-04-12T07:15:58Z","checksum":"17a3e6786d1e930cf0c14a880a6d7e92","relation":"main_file","content_type":"application/pdf","file_size":883851,"file_id":"9319"}],"publication":"Forum of Mathematics, Sigma","citation":{"short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","chicago":"Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>.","apa":"Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>","mla":"Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>.","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.","ama":"Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>","ieee":"L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021."},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd"},{"language":[{"iso":"eng"}],"year":"2020","page":"541-606","publisher":"Springer Nature","article_type":"original","issue":"11","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"RoSe"}],"scopus_import":"1","doi":"10.1007/s00205-020-01548-w","intvolume":"       238","author":[{"orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","last_name":"Bossmann","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"}],"date_created":"2020-07-18T15:06:35Z","volume":238,"oa":1,"month":"11","status":"public","oa_version":"Published Version","_id":"8130","file_date_updated":"2020-12-02T08:50:38Z","ddc":["510"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","chicago":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>.","apa":"Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>","mla":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11, Springer Nature, 2020, pp. 541–606, doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>.","ista":"Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.","ieee":"L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020.","ama":"Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2020;238(11):541-606. doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>"},"publication":"Archive for Rational Mechanics and Analysis","file":[{"date_created":"2020-12-02T08:50:38Z","file_name":"2020_ArchiveRatMech_Bossmann.pdf","access_level":"open_access","creator":"dernst","date_updated":"2020-12-02T08:50:38Z","success":1,"file_size":942343,"file_id":"8826","checksum":"cc67a79a67bef441625fcb1cd031db3d","content_type":"application/pdf","relation":"main_file"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo and Nikolai Leopold are gratefully acknowledged. This work was supported by the German Research Foundation within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems” and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","type":"journal_article","date_updated":"2025-04-14T07:44:05Z","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","publication_status":"published","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000550164400001"],"arxiv":["1907.04547"]},"isi":1,"date_published":"2020-11-01T00:00:00Z","abstract":[{"text":"We study the dynamics of a system of N interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to an interval of length of order ε. The interaction is non-negative and scaled in such a way that its scattering length is of order ε/N, while its range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein condensation. We prove that condensation is preserved by the N-body dynamics, where the time-evolved condensate wave function is the solution of a two-dimensional non-linear equation. The strength of the non-linearity depends on the scaling parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the scattering length of the interaction. In both cases, the coupling parameter depends on the confining potential.","lang":"eng"}],"quality_controlled":"1","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"corr_author":"1","ec_funded":1,"arxiv":1},{"language":[{"iso":"eng"}],"year":"2020","page":"1362-1396","publisher":"Springer Nature","article_type":"original","day":"21","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"RoSe"}],"scopus_import":"1","doi":"10.1007/s10955-020-02500-8","intvolume":"       178","author":[{"first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","orcid":"0000-0002-6854-1343","last_name":"Bossmann","full_name":"Bossmann, Lea"},{"last_name":"Pavlović","full_name":"Pavlović, Nataša","first_name":"Nataša"},{"first_name":"Peter","last_name":"Pickl","full_name":"Pickl, Peter"},{"first_name":"Avy","last_name":"Soffer","full_name":"Soffer, Avy"}],"date_created":"2020-02-23T09:45:51Z","volume":178,"oa":1,"month":"02","status":"public","oa_version":"Published Version","file_date_updated":"2020-11-20T09:26:46Z","_id":"7508","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. 178, 1362–1396.","mla":"Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>, vol. 178, Springer Nature, 2020, pp. 1362–96, doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>.","ama":"Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. 2020;178:1362-1396. doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>","ieee":"L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” <i>Journal of Statistical Physics</i>, vol. 178. Springer Nature, pp. 1362–1396, 2020.","short":"L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics 178 (2020) 1362–1396.","chicago":"Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>.","apa":"Bossmann, L., Pavlović, N., Pickl, P., &#38; Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>"},"publication":"Journal of Statistical Physics","file":[{"file_name":"2020_JournStatPhysics_Bossmann.pdf","date_created":"2020-11-20T09:26:46Z","access_level":"open_access","creator":"dernst","date_updated":"2020-11-20T09:26:46Z","success":1,"file_id":"8780","file_size":576726,"checksum":"643e230bf147e64d9cdb3f6cc573679d","relation":"main_file","content_type":"application/pdf"}],"type":"journal_article","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\nL.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello Porta for helpful discussions. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1. Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and P.P. thank A.S. for his hospitality at CCNU.","date_updated":"2025-04-14T07:44:03Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"publication_status":"published","title":"Higher order corrections to the mean-field description of the dynamics of interacting bosons","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1905.06164"],"isi":["000516342200001"]},"date_published":"2020-02-21T00:00:00Z","isi":1,"abstract":[{"text":"In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.","lang":"eng"}],"quality_controlled":"1","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"corr_author":"1","arxiv":1,"ec_funded":1}]