[{"article_type":"original","publisher":"Springer Nature","quality_controlled":"1","ec_funded":1,"title":"Weak Edgeworth expansion for the mean-field Bose gas","intvolume":"       113","publication_status":"published","date_created":"2023-07-16T22:01:08Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"RoSe"}],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann","first_name":"Lea"},{"orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","first_name":"Sören P","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"}],"issue":"4","_id":"13226","scopus_import":"1","volume":113,"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.","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"}],"doi":"10.1007/s11005-023-01698-4","arxiv":1,"day":"03","isi":1,"external_id":{"isi":["001022878900002"],"arxiv":["2208.00199"]},"date_updated":"2023-12-13T11:31:50Z","citation":{"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.","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>","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>","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>.","short":"L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023)."},"year":"2023","language":[{"iso":"eng"}],"month":"07","article_number":"77","oa_version":"Published Version","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"publication":"Letters in Mathematical Physics","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"date_published":"2023-07-03T00:00:00Z","type":"journal_article"},{"ddc":["530"],"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.","volume":63,"external_id":{"isi":["000809648100002"],"arxiv":["2203.00730"]},"isi":1,"citation":{"ista":"Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102.","short":"L. Bossmann, Journal of Mathematical Physics 63 (2022).","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>.","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>.","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.","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>","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>"},"year":"2022","date_updated":"2023-08-03T12:46:28Z","abstract":[{"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.","lang":"eng"}],"day":"10","arxiv":1,"doi":"10.1063/5.0089983","file_date_updated":"2022-08-11T07:03:02Z","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"AIP Publishing","issue":"6","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea","first_name":"Lea","last_name":"Bossmann"}],"scopus_import":"1","_id":"11783","intvolume":"        63","title":"Low-energy spectrum and dynamics of the weakly interacting Bose gas","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2022-08-11T06:37:52Z","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"file_id":"11784","creator":"dernst","access_level":"open_access","success":1,"relation":"main_file","date_updated":"2022-08-11T07:03:02Z","file_name":"2022_JourMathPhysics_Bossmann.pdf","content_type":"application/pdf","date_created":"2022-08-11T07:03:02Z","file_size":5957888,"checksum":"d0d32c338c1896680174be88c70968fa"}],"type":"journal_article","date_published":"2022-06-10T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Journal of Mathematical Physics","article_number":"061102","month":"06","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Published Version"},{"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.11004"}],"oa":1,"publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"type":"journal_article","date_published":"2021-10-01T00:00:00Z","language":[{"iso":"eng"}],"month":"10","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Preprint","publication":"Pure and Applied Analysis","volume":3,"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.","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."}],"day":"01","arxiv":1,"doi":"10.2140/paa.2021.3.677","external_id":{"arxiv":["1912.11004"]},"year":"2021","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>","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>","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>.","short":"L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726.","mla":"Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>.","ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726."},"date_updated":"2024-02-05T09:26:31Z","article_type":"original","publisher":"Mathematical Sciences Publishers","ec_funded":1,"quality_controlled":"1","page":"677-726","intvolume":"         3","title":"Beyond Bogoliubov dynamics","department":[{"_id":"RoSe"}],"article_processing_charge":"No","date_created":"2024-01-28T23:01:43Z","publication_status":"published","issue":"4","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann","first_name":"Lea"},{"first_name":"Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pickl","first_name":"Peter","full_name":"Pickl, Peter"},{"full_name":"Soffer, Avy","last_name":"Soffer","first_name":"Avy"}],"scopus_import":"1","_id":"14890"},{"_id":"9318","scopus_import":"1","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann","first_name":"Lea","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343"},{"orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","first_name":"Sören P","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","date_created":"2021-04-11T22:01:15Z","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","intvolume":"         9","ec_funded":1,"quality_controlled":"1","file_date_updated":"2021-04-12T07:15:58Z","publisher":"Cambridge University Press","article_type":"original","date_updated":"2023-08-07T14:35:06Z","year":"2021","citation":{"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>","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>","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>.","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.","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","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."},"isi":1,"external_id":{"isi":["000634006900001"]},"doi":"10.1017/fms.2021.22","day":"26","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"}],"volume":9,"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).","ddc":["510"],"publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","oa_version":"Published Version","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"month":"03","article_number":"e28","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2021-03-26T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["20505094"]},"oa":1,"file":[{"file_size":883851,"checksum":"17a3e6786d1e930cf0c14a880a6d7e92","date_created":"2021-04-12T07:15:58Z","file_name":"2021_ForumMath_Bossmann.pdf","content_type":"application/pdf","date_updated":"2021-04-12T07:15:58Z","success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"9319"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"ec_funded":1,"quality_controlled":"1","page":"541-606","file_date_updated":"2020-12-02T08:50:38Z","publisher":"Springer Nature","article_type":"original","scopus_import":"1","_id":"8130","issue":"11","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","last_name":"Bossmann","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea"}],"department":[{"_id":"RoSe"}],"date_created":"2020-07-18T15:06:35Z","article_processing_charge":"Yes (via OA deal)","publication_status":"published","intvolume":"       238","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","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.","volume":238,"ddc":["510"],"year":"2020","citation":{"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>.","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.","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>","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>","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.","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>.","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606."},"date_updated":"2023-09-05T14:19:06Z","external_id":{"isi":["000550164400001"],"arxiv":["1907.04547"]},"isi":1,"day":"01","arxiv":1,"doi":"10.1007/s00205-020-01548-w","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"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Archive for Rational Mechanics and Analysis","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","month":"11","file":[{"file_id":"8826","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access","date_updated":"2020-12-02T08:50:38Z","content_type":"application/pdf","file_name":"2020_ArchiveRatMech_Bossmann.pdf","date_created":"2020-12-02T08:50:38Z","file_size":942343,"checksum":"cc67a79a67bef441625fcb1cd031db3d"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-11-01T00:00:00Z","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"oa":1},{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Journal of Statistical Physics","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"oa_version":"Published Version","month":"02","file":[{"date_updated":"2020-11-20T09:26:46Z","content_type":"application/pdf","file_name":"2020_JournStatPhysics_Bossmann.pdf","date_created":"2020-11-20T09:26:46Z","checksum":"643e230bf147e64d9cdb3f6cc573679d","file_size":576726,"file_id":"8780","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-02-21T00:00:00Z","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"oa":1,"quality_controlled":"1","ec_funded":1,"page":"1362-1396","file_date_updated":"2020-11-20T09:26:46Z","publisher":"Springer Nature","article_type":"original","scopus_import":"1","_id":"7508","author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"full_name":"Pavlović, Nataša","first_name":"Nataša","last_name":"Pavlović"},{"full_name":"Pickl, Peter","last_name":"Pickl","first_name":"Peter"},{"first_name":"Avy","last_name":"Soffer","full_name":"Soffer, Avy"}],"department":[{"_id":"RoSe"}],"date_created":"2020-02-23T09:45:51Z","article_processing_charge":"Yes (via OA deal)","publication_status":"published","intvolume":"       178","title":"Higher order corrections to the mean-field description of the dynamics of interacting bosons","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.","volume":178,"ddc":["510"],"citation":{"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.","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>.","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>","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>","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>.","short":"L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics 178 (2020) 1362–1396."},"year":"2020","date_updated":"2023-08-18T06:37:46Z","external_id":{"isi":["000516342200001"],"arxiv":["1905.06164"]},"isi":1,"day":"21","arxiv":1,"doi":"10.1007/s10955-020-02500-8","abstract":[{"lang":"eng","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."}]}]