[{"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."}],"date_updated":"2023-08-16T11:47:27Z","month":"01","type":"journal_article","oa_version":"Preprint","volume":35,"date_created":"2023-01-29T23:00:59Z","year":"2023","_id":"12430","oa":1,"publication_status":"published","date_published":"2023-01-09T00:00:00Z","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2110.00458","open_access":"1"}],"external_id":{"isi":["000909760300001"],"arxiv":["2110.00458"]},"status":"public","intvolume":"        35","citation":{"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>","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.","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>","short":"M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (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>.","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."},"author":[{"last_name":"Falconi","first_name":"Marco","full_name":"Falconi, Marco"},{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","first_name":"Nikolai K","last_name":"Leopold"},{"last_name":"Mitrouskas","first_name":"David Johannes","full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","first_name":"Sören P","last_name":"Petrat"}],"day":"09","title":"Bogoliubov dynamics and higher-order corrections for the regularized Nelson model","arxiv":1,"article_number":"2350006","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"World Scientific Publishing","department":[{"_id":"RoSe"}],"publication":"Reviews in Mathematical Physics","scopus_import":"1","article_processing_charge":"No","article_type":"original","publication_identifier":{"issn":["0129-055X"]},"doi":"10.1142/S0129055X2350006X","quality_controlled":"1","isi":1,"language":[{"iso":"eng"}],"issue":"4"},{"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"issue":"7","language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"issn":["2157-5045"],"eissn":["1948-206X"]},"quality_controlled":"1","doi":"10.2140/APDE.2021.14.2079","department":[{"_id":"RoSe"}],"publisher":"Mathematical Sciences Publishers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","ec_funded":1,"scopus_import":"1","article_processing_charge":"No","publication":"Analysis and PDE","day":"10","author":[{"last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822"},{"last_name":"Rademacher","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer"}],"title":" The Landau–Pekar equations: Adiabatic theorem and accuracy","arxiv":1,"external_id":{"isi":["000733976600004"],"arxiv":["1904.12532"]},"status":"public","citation":{"ama":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R.  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. 2021;14(7):2079-2100. doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>","ista":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021.  The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.","mla":"Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>.","apa":"Leopold, N. K., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021).  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>","ieee":"N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” <i>Analysis and PDE</i>, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.","chicago":"Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>.","short":"N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100."},"intvolume":"        14","oa":1,"publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1904.12532","open_access":"1"}],"date_published":"2021-11-10T00:00:00Z","year":"2021","acknowledgement":"N. L. and R. S. gratefully acknowledge financial support by the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for stimulating discussions about the time-evolution of a polaron.\r\n","_id":"10738","month":"11","type":"journal_article","oa_version":"Preprint","date_updated":"2023-10-17T11:26:45Z","abstract":[{"text":"We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2.","lang":"eng"}],"page":"2079-2100","date_created":"2022-02-06T23:01:33Z","volume":14},{"external_id":{"arxiv":["2005.02098"]},"status":"public","citation":{"ama":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. 2021;3(4):653-676. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>","mla":"Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>.","ista":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 3(4), 653–676.","apa":"Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>","ieee":"N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021.","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>.","short":"N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676."},"intvolume":"         3","oa":1,"publication_status":"published","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2005.02098","open_access":"1"}],"date_published":"2021-10-01T00:00:00Z","year":"2021","acknowledgement":"Financial support by the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No. 754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227 (N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.), the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel Griesemer for helpful discussions.","_id":"14889","date_updated":"2024-02-05T10:02:45Z","abstract":[{"text":"We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.","lang":"eng"}],"month":"10","oa_version":"Preprint","type":"journal_article","page":"653-676","date_created":"2024-01-28T23:01:43Z","volume":3,"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"issue":"4","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"quality_controlled":"1","doi":"10.2140/paa.2021.3.653","department":[{"_id":"RoSe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Mathematical Sciences Publishers","article_processing_charge":"No","ec_funded":1,"scopus_import":"1","article_type":"original","publication":"Pure and Applied Analysis","day":"01","author":[{"first_name":"Nikolai K","last_name":"Leopold","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K"},{"full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","last_name":"Mitrouskas","first_name":"David Johannes"},{"first_name":"Simone Anna Elvira","last_name":"Rademacher","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"title":"Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron","arxiv":1},{"_id":"9246","year":"2021","acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","date_created":"2021-03-14T23:01:34Z","file_date_updated":"2021-03-22T08:31:29Z","volume":240,"date_updated":"2023-08-07T14:12:27Z","abstract":[{"lang":"eng","text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order."}],"month":"02","oa_version":"Published Version","type":"journal_article","page":"383-417","citation":{"short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417.","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>.","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240. Springer Nature, pp. 383–417, 2021.","apa":"Leopold, N. K., Mitrouskas, D. J., &#38; Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>","mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240, Springer Nature, 2021, pp. 383–417, doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>.","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. 2021;240:383-417. doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>"},"intvolume":"       240","external_id":{"isi":["000622226200001"],"arxiv":["2001.03993"]},"status":"public","ddc":["510"],"date_published":"2021-02-26T00:00:00Z","has_accepted_license":"1","oa":1,"publication_status":"published","article_processing_charge":"No","scopus_import":"1","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publication":"Archive for Rational Mechanics and Analysis","department":[{"_id":"RoSe"}],"publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","arxiv":1,"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"checksum":"23449e44dc5132501a5c86e70638800f","date_updated":"2021-03-22T08:31:29Z","file_id":"9270","access_level":"open_access","date_created":"2021-03-22T08:31:29Z","success":1,"file_name":"2021_ArchRationalMechAnal_Leopold.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":558006}],"day":"26","author":[{"full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822","last_name":"Leopold","first_name":"Nikolai K"},{"last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"}],"language":[{"iso":"eng"}],"isi":1,"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","doi":"10.1007/s00205-021-01616-9","publication_identifier":{"issn":["00039527"],"eissn":["14320673"]}},{"isi":1,"language":[{"iso":"eng"}],"issue":"10","project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"doi":"10.1007/s00023-019-00828-w","quality_controlled":"1","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication":"Annales Henri Poincare","scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","department":[{"_id":"RoSe"}],"arxiv":1,"title":"Mean-field dynamics for the Nelson model with fermions","author":[{"first_name":"Nikolai K","last_name":"Leopold","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822"},{"orcid":"0000-0002-9166-5889","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P","last_name":"Petrat","first_name":"Sören P"}],"day":"01","file":[{"checksum":"b6dbf0d837d809293d449adf77138904","file_id":"6801","date_updated":"2020-07-14T12:47:40Z","access_level":"open_access","date_created":"2019-08-12T12:05:58Z","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","creator":"dernst","file_size":681139,"relation":"main_file","content_type":"application/pdf"}],"intvolume":"        20","citation":{"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>","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>","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>.","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."},"status":"public","external_id":{"arxiv":["1807.06781"],"isi":["000487036900008"]},"ddc":["510"],"date_published":"2019-10-01T00:00:00Z","publication_status":"published","oa":1,"has_accepted_license":"1","_id":"6788","year":"2019","volume":20,"file_date_updated":"2020-07-14T12:47:40Z","date_created":"2019-08-11T21:59:21Z","page":"3471–3508","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"}],"date_updated":"2023-08-29T07:09:06Z","month":"10","type":"journal_article","oa_version":"Published Version"},{"title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","file":[{"file_name":"2019_CommMathPhys_Jeblick.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":884469,"checksum":"cd283b475dd739e04655315abd46f528","date_updated":"2020-07-14T12:47:49Z","file_id":"7101","access_level":"open_access","date_created":"2019-11-25T08:11:11Z"}],"day":"08","author":[{"full_name":"Jeblick, Maximilian","first_name":"Maximilian","last_name":"Jeblick"},{"full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","last_name":"Leopold"},{"full_name":"Pickl, Peter","first_name":"Peter","last_name":"Pickl"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Communications in Mathematical Physics","department":[{"_id":"RoSe"}],"publisher":"Springer Nature","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","doi":"10.1007/s00220-019-03599-x","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"language":[{"iso":"eng"}],"issue":"1","isi":1,"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"}],"date_created":"2019-11-25T08:08:02Z","file_date_updated":"2020-07-14T12:47:49Z","volume":372,"abstract":[{"text":"We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.","lang":"eng"}],"date_updated":"2023-09-06T10:47:43Z","month":"11","oa_version":"Published Version","type":"journal_article","page":"1-69","_id":"7100","year":"2019","acknowledgement":"OA fund by IST Austria","date_published":"2019-11-08T00:00:00Z","ddc":["510"],"has_accepted_license":"1","publication_status":"published","oa":1,"citation":{"chicago":"Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>.","ieee":"M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69.","ama":"Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. 2019;372(1):1-69. doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>","apa":"Jeblick, M., Leopold, N. K., &#38; Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>","mla":"Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>.","ista":"Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69."},"intvolume":"       372","status":"public","external_id":{"isi":["000495193700002"]}},{"volume":270,"date_created":"2018-12-11T11:44:08Z","page":"185 - 214","date_updated":"2021-01-12T06:48:16Z","abstract":[{"text":"We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm.","lang":"eng"}],"oa_version":"Preprint","type":"conference","month":"10","_id":"11","year":"2018","date_published":"2018-10-27T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.10843"}],"oa":1,"publication_status":"published","intvolume":"       270","citation":{"short":"N.K. Leopold, P. Pickl, in:, Springer, 2018, pp. 185–214.","ieee":"N. K. Leopold and P. Pickl, “Mean-field limits of particles in interaction with quantised radiation fields,” presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany, 2018, vol. 270, pp. 185–214.","chicago":"Leopold, Nikolai K, and Peter Pickl. “Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields,” 270:185–214. Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-030-01602-9_9\">https://doi.org/10.1007/978-3-030-01602-9_9</a>.","ista":"Leopold NK, Pickl P. 2018. Mean-field limits of particles in interaction with quantised radiation fields. MaLiQS: Macroscopic Limits of Quantum Systems vol. 270, 185–214.","mla":"Leopold, Nikolai K., and Peter Pickl. <i>Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields</i>. Vol. 270, Springer, 2018, pp. 185–214, doi:<a href=\"https://doi.org/10.1007/978-3-030-01602-9_9\">10.1007/978-3-030-01602-9_9</a>.","apa":"Leopold, N. K., &#38; Pickl, P. (2018). Mean-field limits of particles in interaction with quantised radiation fields (Vol. 270, pp. 185–214). Presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany: Springer. <a href=\"https://doi.org/10.1007/978-3-030-01602-9_9\">https://doi.org/10.1007/978-3-030-01602-9_9</a>","ama":"Leopold NK, Pickl P. Mean-field limits of particles in interaction with quantised radiation fields. In: Vol 270. Springer; 2018:185-214. doi:<a href=\"https://doi.org/10.1007/978-3-030-01602-9_9\">10.1007/978-3-030-01602-9_9</a>"},"status":"public","external_id":{"arxiv":["1806.10843"]},"arxiv":1,"title":"Mean-field limits of particles in interaction with quantised radiation fields","publist_id":"8045","author":[{"last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","last_name":"Pickl","full_name":"Pickl, Peter"}],"day":"27","scopus_import":1,"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","department":[{"_id":"RoSe"}],"doi":"10.1007/978-3-030-01602-9_9","quality_controlled":"1","conference":{"end_date":"2017-04-01","location":"Munich, Germany","name":"MaLiQS: Macroscopic Limits of Quantum Systems","start_date":"2017-03-30"},"language":[{"iso":"eng"}],"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}]},{"oa":1,"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01204"}],"date_published":"2018-12-12T00:00:00Z","status":"public","external_id":{"arxiv":["1809.01204"],"isi":["000452992700008"]},"citation":{"chicago":"Yakaboylu, Enderalp, Bikashkali Midya, Andreas Deuchert, Nikolai K Leopold, and Mikhail Lemeshko. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” <i>Physical Review B</i>. American Physical Society, 2018. <a href=\"https://doi.org/10.1103/physrevb.98.224506\">https://doi.org/10.1103/physrevb.98.224506</a>.","ieee":"E. Yakaboylu, B. Midya, A. Deuchert, N. K. Leopold, and M. Lemeshko, “Theory of the rotating polaron: Spectrum and self-localization,” <i>Physical Review B</i>, vol. 98, no. 22. American Physical Society, 2018.","short":"E. Yakaboylu, B. Midya, A. Deuchert, N.K. Leopold, M. Lemeshko, Physical Review B 98 (2018).","ama":"Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. Theory of the rotating polaron: Spectrum and self-localization. <i>Physical Review B</i>. 2018;98(22). doi:<a href=\"https://doi.org/10.1103/physrevb.98.224506\">10.1103/physrevb.98.224506</a>","apa":"Yakaboylu, E., Midya, B., Deuchert, A., Leopold, N. K., &#38; Lemeshko, M. (2018). Theory of the rotating polaron: Spectrum and self-localization. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.98.224506\">https://doi.org/10.1103/physrevb.98.224506</a>","ista":"Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. 2018. Theory of the rotating polaron: Spectrum and self-localization. Physical Review B. 98(22), 224506.","mla":"Yakaboylu, Enderalp, et al. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” <i>Physical Review B</i>, vol. 98, no. 22, 224506, American Physical Society, 2018, doi:<a href=\"https://doi.org/10.1103/physrevb.98.224506\">10.1103/physrevb.98.224506</a>."},"intvolume":"        98","oa_version":"Preprint","type":"journal_article","month":"12","date_updated":"2023-09-19T14:29:03Z","abstract":[{"lang":"eng","text":"We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a “rotating polaron,” which can be used to model, e.g., a rotating molecule immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian of the rotating polaron and study its spectrum in the weak- and strong-coupling regimes using a combination of variational, diagrammatic, and mean-field approaches. We reveal how the coupling between linear and angular momenta affects stable quasiparticle states, and demonstrate that internal rotation leads to an enhanced self-localization in the translational degrees of freedom."}],"date_created":"2019-02-14T10:37:09Z","volume":98,"year":"2018","_id":"5983","publication_identifier":{"eissn":["2469-9969"],"issn":["2469-9950"]},"quality_controlled":"1","doi":"10.1103/physrevb.98.224506","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"},{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"issue":"22","language":[{"iso":"eng"}],"isi":1,"day":"12","author":[{"full_name":"Yakaboylu, Enderalp","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5973-0874","last_name":"Yakaboylu","first_name":"Enderalp"},{"id":"456187FC-F248-11E8-B48F-1D18A9856A87","full_name":"Midya, Bikashkali","first_name":"Bikashkali","last_name":"Midya"},{"first_name":"Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas"},{"last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822"},{"last_name":"Lemeshko","first_name":"Mikhail","full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802"}],"article_number":"224506","title":"Theory of the rotating polaron: Spectrum and self-localization","arxiv":1,"department":[{"_id":"MiLe"},{"_id":"RoSe"}],"publisher":"American Physical Society","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","publication":"Physical Review B"}]