[{"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.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"quality_controlled":"1","_id":"13226","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"date_updated":"2023-12-13T11:31:50Z","volume":113,"article_processing_charge":"Yes (via OA deal)","arxiv":1,"author":[{"first_name":"Lea","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"last_name":"Petrat","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","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."}],"publication_status":"published","citation":{"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>","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.","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.","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>."},"isi":1,"article_number":"77","external_id":{"isi":["001022878900002"],"arxiv":["2208.00199"]},"title":"Weak Edgeworth expansion for the mean-field Bose gas","ec_funded":1,"year":"2023","doi":"10.1007/s11005-023-01698-4","issue":"4","publication":"Letters in Mathematical Physics","status":"public","intvolume":"       113","type":"journal_article","day":"03","date_created":"2023-07-16T22:01:08Z","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","article_type":"original","date_published":"2023-07-03T00:00:00Z","month":"07"},{"issue":"4","publication":"Reviews in Mathematical Physics","intvolume":"        35","status":"public","day":"09","type":"journal_article","date_created":"2023-01-29T23:00:59Z","department":[{"_id":"RoSe"}],"publisher":"World Scientific Publishing","scopus_import":"1","language":[{"iso":"eng"}],"month":"01","date_published":"2023-01-09T00:00:00Z","article_type":"original","_id":"12430","publication_identifier":{"issn":["0129-055X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Preprint","arxiv":1,"volume":35,"date_updated":"2023-08-16T11:47:27Z","oa":1,"article_processing_charge":"No","abstract":[{"lang":"eng","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."}],"author":[{"last_name":"Falconi","full_name":"Falconi, Marco","first_name":"Marco"},{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","last_name":"Leopold","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","first_name":"Nikolai K"},{"first_name":"David Johannes","last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"full_name":"Petrat, Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","citation":{"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.","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>","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>.","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>.","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>","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)."},"isi":1,"article_number":"2350006","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2110.00458"}],"title":"Bogoliubov dynamics and higher-order corrections for the regularized Nelson model","external_id":{"isi":["000909760300001"],"arxiv":["2110.00458"]},"year":"2023","doi":"10.1142/S0129055X2350006X"},{"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."}],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","last_name":"Bossmann","first_name":"Lea"},{"orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","last_name":"Petrat","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","full_name":"Pickl, Peter","last_name":"Pickl"},{"full_name":"Soffer, Avy","last_name":"Soffer","first_name":"Avy"}],"publication_status":"published","citation":{"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.","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>.","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."},"_id":"14890","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"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.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"oa_version":"Preprint","arxiv":1,"volume":3,"date_updated":"2024-02-05T09:26:31Z","oa":1,"article_processing_charge":"No","external_id":{"arxiv":["1912.11004"]},"title":"Beyond Bogoliubov dynamics","year":"2021","doi":"10.2140/paa.2021.3.677","ec_funded":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.11004","open_access":"1"}],"intvolume":"         3","status":"public","day":"01","type":"journal_article","issue":"4","publication":"Pure and Applied Analysis","page":"677-726","publisher":"Mathematical Sciences Publishers","scopus_import":"1","language":[{"iso":"eng"}],"month":"10","date_published":"2021-10-01T00:00:00Z","article_type":"original","date_created":"2024-01-28T23:01:43Z","department":[{"_id":"RoSe"}]},{"ec_funded":1,"doi":"10.1017/fms.2021.22","year":"2021","title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","external_id":{"isi":["000634006900001"]},"isi":1,"article_number":"e28","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"citation":{"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>.","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>","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.","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>","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.","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>."},"publication_status":"published","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","last_name":"Bossmann"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","first_name":"Sören P"},{"first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","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."}],"article_processing_charge":"Yes (via OA deal)","volume":9,"oa":1,"date_updated":"2023-08-07T14:35:06Z","project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"oa_version":"Published Version","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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).","publication_identifier":{"eissn":["20505094"]},"_id":"9318","article_type":"original","date_published":"2021-03-26T00:00:00Z","month":"03","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Cambridge University Press","department":[{"_id":"RoSe"}],"has_accepted_license":"1","date_created":"2021-04-11T22:01:15Z","file":[{"date_updated":"2021-04-12T07:15:58Z","access_level":"open_access","file_name":"2021_ForumMath_Bossmann.pdf","file_size":883851,"date_created":"2021-04-12T07:15:58Z","checksum":"17a3e6786d1e930cf0c14a880a6d7e92","content_type":"application/pdf","relation":"main_file","file_id":"9319","creator":"dernst","success":1}],"type":"journal_article","day":"26","status":"public","intvolume":"         9","file_date_updated":"2021-04-12T07:15:58Z","publication":"Forum of Mathematics, Sigma"},{"title":"Mean-field dynamics for the Nelson model with fermions","external_id":{"isi":["000487036900008"],"arxiv":["1807.06781"]},"ec_funded":1,"year":"2019","doi":"10.1007/s00023-019-00828-w","ddc":["510"],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"author":[{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","last_name":"Leopold"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","last_name":"Petrat","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","first_name":"Sören P"}],"abstract":[{"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.","lang":"eng"}],"publication_status":"published","citation":{"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>.","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>","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>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","quality_controlled":"1","_id":"6788","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"date_updated":"2023-08-29T07:09:06Z","volume":20,"oa":1,"article_processing_charge":"Yes (via OA deal)","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","date_published":"2019-10-01T00:00:00Z","article_type":"original","month":"10","file":[{"access_level":"open_access","date_updated":"2020-07-14T12:47:40Z","file_size":681139,"file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","checksum":"b6dbf0d837d809293d449adf77138904","date_created":"2019-08-12T12:05:58Z","relation":"main_file","content_type":"application/pdf","file_id":"6801","creator":"dernst"}],"date_created":"2019-08-11T21:59:21Z","department":[{"_id":"RoSe"}],"has_accepted_license":"1","status":"public","intvolume":"        20","type":"journal_article","day":"01","page":"3471–3508","file_date_updated":"2020-07-14T12:47:40Z","issue":"10","publication":"Annales Henri Poincare"},{"author":[{"first_name":"Volker","full_name":"Bach, Volker","last_name":"Bach"},{"first_name":"Sébastien","full_name":"Breteaux, Sébastien","last_name":"Breteaux"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","last_name":"Petrat","first_name":"Sören P"},{"full_name":"Pickl, Peter","last_name":"Pickl","first_name":"Peter"},{"last_name":"Tzaneteas","full_name":"Tzaneteas, Tim","first_name":"Tim"}],"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"}],"publication_status":"published","citation":{"short":"V. Bach, S. Breteaux, S.P. Petrat, P. Pickl, T. Tzaneteas, Journal de Mathématiques Pures et Appliquées 105 (2016) 1–30.","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.","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>","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>.","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.","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>"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","oa_version":"Published Version","_id":"1436","oa":1,"volume":105,"date_updated":"2021-01-12T06:50:43Z","publist_id":"5763","pubrep_id":"581","title":"Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction","ec_funded":1,"year":"2016","doi":"10.1016/j.matpur.2015.09.003","ddc":["510","530"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"status":"public","intvolume":"       105","type":"journal_article","day":"01","page":"1 - 30","file_date_updated":"2020-07-14T12:44:54Z","issue":"1","publication":"Journal de Mathématiques Pures et Appliquées","language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":1,"date_published":"2016-01-01T00:00:00Z","month":"01","date_created":"2018-12-11T11:52:00Z","file":[{"date_created":"2018-12-12T10:10:36Z","checksum":"c5afe1f6935bc7f2b546adbde1d31a35","file_name":"IST-2016-581-v1+1_1-s2.0-S0021782415001191-main.pdf","file_size":658491,"date_updated":"2020-07-14T12:44:54Z","access_level":"open_access","file_id":"4825","creator":"system","content_type":"application/pdf","relation":"main_file"}],"department":[{"_id":"RoSe"}],"has_accepted_license":"1"},{"author":[{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat","full_name":"Petrat, Sören P"},{"full_name":"Pickl, Peter","last_name":"Pickl","first_name":"Peter"}],"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."}],"citation":{"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.","short":"S.P. Petrat, P. Pickl, Mathematical Physics, Analysis and Geometry 19 (2016).","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>","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>.","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>.","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>","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."},"publication_status":"published","quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","_id":"1493","article_processing_charge":"Yes (via OA deal)","oa":1,"volume":19,"publist_id":"5690","date_updated":"2021-01-12T06:51:08Z","title":"A new method and a new scaling for deriving fermionic mean-field dynamics","pubrep_id":"514","ec_funded":1,"year":"2016","doi":"10.1007/s11040-016-9204-2","ddc":["510","530"],"article_number":"3","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","intvolume":"        19","type":"journal_article","day":"01","file_date_updated":"2020-07-14T12:44:58Z","publication":"Mathematical Physics, Analysis and Geometry","issue":"1","language":[{"iso":"eng"}],"scopus_import":1,"publisher":"Springer","date_published":"2016-03-01T00:00:00Z","month":"03","file":[{"access_level":"open_access","date_updated":"2020-07-14T12:44:58Z","file_size":911310,"file_name":"IST-2016-514-v1+1_s11040-016-9204-2.pdf","checksum":"eb5d2145ef0d377c4f78bf06e18f4529","date_created":"2018-12-12T10:16:55Z","relation":"main_file","content_type":"application/pdf","creator":"system","file_id":"5246"}],"date_created":"2018-12-11T11:52:20Z","department":[{"_id":"RoSe"}],"has_accepted_license":"1"}]