[{"article_type":"original","department":[{"_id":"RoSe"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-04-14T22:01:02Z","month":"04","dataavailabilitystatement":"Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.","_id":"15318","intvolume":"       191","file_date_updated":"2024-04-16T11:09:37Z","publication":"Journal of Statistical Physics","oa_version":"Published Version","oa":1,"date_updated":"2026-09-17T11:05:18Z","file":[{"file_name":"2024_JourStatPhysics_Bossmann.pdf","creator":"dernst","success":1,"date_updated":"2024-04-16T11:09:37Z","file_id":"15325","date_created":"2024-04-16T11:09:37Z","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_size":398665,"checksum":"839242a9ec1c01158112de25f196e60d"}],"isi":1,"das_tickbox":"1","year":"2024","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":191,"researchdata_availability":"not applicable","citation":{"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>","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.","short":"L. Bossmann, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Journal of Statistical Physics 191 (2024).","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.","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>"},"publication_status":"published","doi":"10.1007/s10955-024-03260-5","publisher":"Springer Nature","status":"public","issue":"4","quality_controlled":"1","abstract":[{"lang":"eng","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."}],"title":"A note on the binding energy for Bosons in the mean-field limit","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.","fulldoi":"https://doi.org/10.1007/s10955-024-03260-5","ddc":["510"],"has_accepted_license":"1","arxiv":1,"external_id":{"arxiv":["2307.13115"],"isi":["001197663100002"]},"date_published":"2024-04-06T00:00:00Z","language":[{"iso":"eng"}],"supplementarymaterial":"no","article_number":"48","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","full_name":"Bossmann, Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea"},{"full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","last_name":"Leopold","orcid":"0000-0002-0495-6822"},{"last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat"}],"scopus_import":"1","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"day":"06","article_processing_charge":"Yes (via OA deal)","type":"journal_article"},{"intvolume":"        35","oa_version":"Preprint","publication":"Reviews in Mathematical Physics","oa":1,"date_updated":"2023-08-16T11:47:27Z","isi":1,"article_type":"original","department":[{"_id":"RoSe"}],"date_created":"2023-01-29T23:00:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","_id":"12430","publisher":"World Scientific Publishing","status":"public","issue":"4","quality_controlled":"1","title":"Bogoliubov dynamics and higher-order corrections for the regularized Nelson model","abstract":[{"text":"We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.","lang":"eng"}],"year":"2023","volume":35,"citation":{"ama":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. 2023;35(4). doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>","mla":"Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4, 2350006, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>.","ista":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 35(4), 2350006.","short":"M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (2023).","ieee":"M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov dynamics and higher-order corrections for the regularized Nelson model,” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4. World Scientific Publishing, 2023.","chicago":"Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>.","apa":"Falconi, M., Leopold, N. K., Mitrouskas, D. J., &#38; Petrat, S. P. (2023). Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>"},"publication_status":"published","doi":"10.1142/S0129055X2350006X","arxiv":1,"external_id":{"arxiv":["2110.00458"],"isi":["000909760300001"]},"date_published":"2023-01-09T00:00:00Z","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1142/S0129055X2350006X","day":"09","article_processing_charge":"No","type":"journal_article","article_number":"2350006","author":[{"full_name":"Falconi, Marco","first_name":"Marco","last_name":"Falconi"},{"last_name":"Leopold","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K"},{"last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"orcid":"0000-0002-9166-5889","last_name":"Petrat","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P"}],"scopus_import":"1","publication_identifier":{"issn":["0129-055X"]},"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2110.00458"}]},{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2023","volume":113,"OA_place":"publisher","publication_status":"published","citation":{"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>","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>.","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.","short":"L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).","ista":"Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77.","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>.","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>"},"OA_type":"hybrid","doi":"10.1007/s11005-023-01698-4","status":"public","issue":"4","publisher":"Springer Nature","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"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"}],"title":"Weak Edgeworth expansion for the mean-field Bose gas","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.","department":[{"_id":"RoSe"}],"article_type":"original","date_created":"2023-07-16T22:01:08Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","ec_funded":1,"_id":"13226","file_date_updated":"2025-06-25T06:20:02Z","intvolume":"       113","oa_version":"Published Version","publication":"Letters in Mathematical Physics","file":[{"file_name":"2023_LettersMathPhysics_Bossmann.pdf","creator":"dernst","file_id":"19898","date_updated":"2025-06-25T06:20:02Z","success":1,"access_level":"open_access","content_type":"application/pdf","date_created":"2025-06-25T06:20:02Z","file_size":586698,"checksum":"995c902a989a6769fd3db456cfd41111","relation":"main_file"}],"date_updated":"2025-06-25T06:20:15Z","isi":1,"oa":1,"corr_author":"1","article_number":"77","author":[{"last_name":"Bossmann","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"scopus_import":"1","day":"03","article_processing_charge":"Yes (via OA deal)","type":"journal_article","ddc":["510"],"fulldoi":"https://doi.org/10.1007/s11005-023-01698-4","has_accepted_license":"1","arxiv":1,"date_published":"2023-07-03T00:00:00Z","external_id":{"arxiv":["2208.00199"],"isi":["001022878900002"]},"language":[{"iso":"eng"}]},{"year":"2021","volume":3,"publication_status":"published","citation":{"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.","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.","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>.","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>"},"doi":"10.2140/paa.2021.3.677","status":"public","issue":"4","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"}],"publisher":"Mathematical Sciences Publishers","quality_controlled":"1","title":"Beyond Bogoliubov dynamics","abstract":[{"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.","lang":"eng"}],"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.","department":[{"_id":"RoSe"}],"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-01-28T23:01:43Z","month":"10","ec_funded":1,"_id":"14890","intvolume":"         3","publication":"Pure and Applied Analysis","oa_version":"Preprint","date_updated":"2025-04-14T07:44:02Z","oa":1,"corr_author":"1","page":"677-726","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","full_name":"Bossmann, Lea"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","full_name":"Petrat, Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889"},{"first_name":"Peter","full_name":"Pickl, Peter","last_name":"Pickl"},{"last_name":"Soffer","first_name":"Avy","full_name":"Soffer, Avy"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.11004","open_access":"1"}],"scopus_import":"1","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"day":"01","article_processing_charge":"No","type":"journal_article","fulldoi":"https://doi.org/10.2140/paa.2021.3.677","arxiv":1,"external_id":{"arxiv":["1912.11004"]},"date_published":"2021-10-01T00:00:00Z","language":[{"iso":"eng"}]},{"fulldoi":"https://doi.org/10.1017/fms.2021.22","ddc":["510"],"has_accepted_license":"1","language":[{"iso":"eng"}],"external_id":{"isi":["000634006900001"]},"date_published":"2021-03-26T00:00:00Z","author":[{"orcid":"0000-0002-6854-1343","last_name":"Bossmann","full_name":"Bossmann, Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea"},{"orcid":"0000-0002-9166-5889","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","full_name":"Petrat, Sören P"},{"full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"publication_identifier":{"eissn":["2050-5094"]},"scopus_import":"1","article_number":"e28","article_processing_charge":"Yes (via OA deal)","type":"journal_article","day":"26","month":"03","ec_funded":1,"_id":"9318","article_type":"original","department":[{"_id":"RoSe"}],"date_created":"2021-04-11T22:01:15Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"file":[{"creator":"dernst","file_name":"2021_ForumMath_Bossmann.pdf","file_id":"9319","date_updated":"2021-04-12T07:15:58Z","success":1,"content_type":"application/pdf","date_created":"2021-04-12T07:15:58Z","access_level":"open_access","relation":"main_file","file_size":883851,"checksum":"17a3e6786d1e930cf0c14a880a6d7e92"}],"isi":1,"date_updated":"2026-04-02T14:02:29Z","intvolume":"         9","file_date_updated":"2021-04-12T07:15:58Z","oa_version":"Published Version","publication":"Forum of Mathematics, Sigma","doi":"10.1017/fms.2021.22","year":"2021","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":9,"citation":{"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>","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>.","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>","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","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."},"publication_status":"published","title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","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"}],"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).","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"publisher":"Cambridge University Press","status":"public","quality_controlled":"1"},{"arxiv":1,"external_id":{"isi":["000487036900008"],"arxiv":["1807.06781"]},"date_published":"2019-10-01T00:00:00Z","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1007/s00023-019-00828-w","ddc":["510"],"has_accepted_license":"1","day":"01","article_processing_charge":"Yes (via OA deal)","type":"journal_article","corr_author":"1","page":"3471–3508","author":[{"full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","last_name":"Leopold","orcid":"0000-0002-0495-6822"},{"full_name":"Petrat, Sören P","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","last_name":"Petrat"}],"publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"scopus_import":"1","intvolume":"        20","file_date_updated":"2020-07-14T12:47:40Z","publication":"Annales Henri Poincare","oa_version":"Published Version","oa":1,"isi":1,"file":[{"date_updated":"2020-07-14T12:47:40Z","file_id":"6801","creator":"dernst","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","relation":"main_file","checksum":"b6dbf0d837d809293d449adf77138904","file_size":681139,"date_created":"2019-08-12T12:05:58Z","content_type":"application/pdf","access_level":"open_access"}],"date_updated":"2026-07-28T13:24:14Z","article_type":"original","department":[{"_id":"RoSe"}],"date_created":"2019-08-11T21:59:21Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"10","_id":"6788","ec_funded":1,"publisher":"Springer Nature","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"status":"public","issue":"10","quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations."}],"title":"Mean-field dynamics for the Nelson model with fermions","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). We would like to thank Peter Pickl and Robert Seiringer for fruitful discussions, and the anonymous referees for their valuable comments and suggestions. Moreover, we would like to thank Niels Benedikter and László Erdős for helpful remarks about the semiclassical structure and the Schrödinger–Klein–Gordon equations. N. L. gratefully acknowledges financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227) and funding for his stay at Princeton University from the project “Effective One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation and Properties” (Project No. 318342445) of the German Research Foundation (DFG). S. P. gratefully acknowledges support from the German Academic Exchange Service (DAAD) and the National Science Foundation under Agreement No. DMS-1128155. Moreover, we would like to thank Princeton University and the Institute for Advanced Study for their hospitality. S. P. would additionally like to thank the University of Washington for hospitality.","year":"2019","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":20,"citation":{"apa":"Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>","chicago":"Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>.","ieee":"N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019.","short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.","mla":"Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>.","ama":"Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>"},"publication_status":"published","OA_place":"publisher","OA_type":"hybrid","doi":"10.1007/s00023-019-00828-w"},{"doi":"10.1016/j.matpur.2015.09.003","volume":105,"tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"year":"2016","publication_status":"published","citation":{"mla":"Bach, Volker, et al. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 105, no. 1, Elsevier, 2016, pp. 1–30, doi:<a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">10.1016/j.matpur.2015.09.003</a>.","ama":"Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. <i>Journal de Mathématiques Pures et Appliquées</i>. 2016;105(1):1-30. doi:<a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">10.1016/j.matpur.2015.09.003</a>","ista":"Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. 2016. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 105(1), 1–30.","ieee":"V. Bach, S. Breteaux, S. P. Petrat, P. Pickl, and T. Tzaneteas, “Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction,” <i>Journal de Mathématiques Pures et Appliquées</i>, vol. 105, no. 1. Elsevier, pp. 1–30, 2016.","short":"V. Bach, S. Breteaux, S.P. Petrat, P. Pickl, T. Tzaneteas, Journal de Mathématiques Pures et Appliquées 105 (2016) 1–30.","apa":"Bach, V., Breteaux, S., Petrat, S. P., Pickl, P., &#38; Tzaneteas, T. (2016). Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">https://doi.org/10.1016/j.matpur.2015.09.003</a>","chicago":"Bach, Volker, Sébastien Breteaux, Sören P Petrat, Peter Pickl, and Tim Tzaneteas. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” <i>Journal de Mathématiques Pures et Appliquées</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.matpur.2015.09.003\">https://doi.org/10.1016/j.matpur.2015.09.003</a>."},"title":"Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction","abstract":[{"text":"We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.","lang":"eng"}],"publisher":"Elsevier","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"issue":"1","status":"public","quality_controlled":"1","month":"01","_id":"1436","ec_funded":1,"department":[{"_id":"RoSe"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:52:00Z","oa":1,"file":[{"file_id":"4825","date_updated":"2020-07-14T12:44:54Z","creator":"system","file_name":"IST-2016-581-v1+1_1-s2.0-S0021782415001191-main.pdf","relation":"main_file","file_size":658491,"checksum":"c5afe1f6935bc7f2b546adbde1d31a35","content_type":"application/pdf","date_created":"2018-12-12T10:10:36Z","access_level":"open_access"}],"date_updated":"2025-09-18T12:31:28Z","isi":1,"intvolume":"       105","file_date_updated":"2020-07-14T12:44:54Z","publication":"Journal de Mathématiques Pures et Appliquées","oa_version":"Published Version","publist_id":"5763","author":[{"first_name":"Volker","full_name":"Bach, Volker","last_name":"Bach"},{"first_name":"Sébastien","full_name":"Breteaux, Sébastien","last_name":"Breteaux"},{"full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat"},{"last_name":"Pickl","first_name":"Peter","full_name":"Pickl, Peter"},{"last_name":"Tzaneteas","full_name":"Tzaneteas, Tim","first_name":"Tim"}],"scopus_import":"1","pubrep_id":"581","page":"1 - 30","article_processing_charge":"No","type":"journal_article","day":"01","fulldoi":"https://doi.org/10.1016/j.matpur.2015.09.003","ddc":["510","530"],"has_accepted_license":"1","language":[{"iso":"eng"}],"date_published":"2016-01-01T00:00:00Z","external_id":{"isi":["000366773900001"]}},{"department":[{"_id":"RoSe"}],"date_created":"2018-12-11T11:52:20Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"03","ec_funded":1,"_id":"1493","file_date_updated":"2020-07-14T12:44:58Z","intvolume":"        19","oa_version":"Published Version","publication":"Mathematical Physics, Analysis and Geometry","isi":1,"file":[{"checksum":"eb5d2145ef0d377c4f78bf06e18f4529","file_size":911310,"relation":"main_file","access_level":"open_access","date_created":"2018-12-12T10:16:55Z","content_type":"application/pdf","file_id":"5246","date_updated":"2020-07-14T12:44:58Z","file_name":"IST-2016-514-v1+1_s11040-016-9204-2.pdf","creator":"system"}],"date_updated":"2025-09-18T11:12:46Z","oa":1,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":19,"year":"2016","citation":{"apa":"Petrat, S. P., &#38; Pickl, P. (2016). A new method and a new scaling for deriving fermionic mean-field dynamics. <i>Mathematical Physics, Analysis and Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s11040-016-9204-2\">https://doi.org/10.1007/s11040-016-9204-2</a>","chicago":"Petrat, Sören P, and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11040-016-9204-2\">https://doi.org/10.1007/s11040-016-9204-2</a>.","ieee":"S. P. Petrat and P. Pickl, “A new method and a new scaling for deriving fermionic mean-field dynamics,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 1. Springer, 2016.","short":"S.P. Petrat, P. Pickl, Mathematical Physics, Analysis and Geometry 19 (2016).","ista":"Petrat SP, Pickl P. 2016. A new method and a new scaling for deriving fermionic mean-field dynamics. Mathematical Physics, Analysis and Geometry. 19(1), 3.","mla":"Petrat, Sören P., and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 19, no. 1, 3, Springer, 2016, doi:<a href=\"https://doi.org/10.1007/s11040-016-9204-2\">10.1007/s11040-016-9204-2</a>.","ama":"Petrat SP, Pickl P. A new method and a new scaling for deriving fermionic mean-field dynamics. <i>Mathematical Physics, Analysis and Geometry</i>. 2016;19(1). doi:<a href=\"https://doi.org/10.1007/s11040-016-9204-2\">10.1007/s11040-016-9204-2</a>"},"publication_status":"published","doi":"10.1007/s11040-016-9204-2","status":"public","issue":"1","publisher":"Springer","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence."}],"title":"A new method and a new scaling for deriving fermionic mean-field dynamics","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","ddc":["510","530"],"fulldoi":"https://doi.org/10.1007/s11040-016-9204-2","has_accepted_license":"1","external_id":{"isi":["000374267300003"]},"date_published":"2016-03-01T00:00:00Z","language":[{"iso":"eng"}],"pubrep_id":"514","corr_author":"1","article_number":"3","author":[{"orcid":"0000-0002-9166-5889","last_name":"Petrat","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"}],"publist_id":"5690","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","type":"journal_article"}]