[{"publication":"Letters in Mathematical Physics","abstract":[{"lang":"eng","text":"The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere, we provide a class of initial data for which the associated effective Hamiltonian\r\nhas a uniform spectral gap for all times. For such initial data, this allows us to extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations and their derivation\r\nfrom the Fröhlich model obtained in previous works to larger times."}],"intvolume":"       111","has_accepted_license":"1","publication_status":"published","title":"Persistence of the spectral gap for the Landau–Pekar equations","ec_funded":1,"day":"11","quality_controlled":"1","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530"},{"full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","last_name":"Rademacher"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","isi":1,"citation":{"ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the spectral gap for the Landau–Pekar equations,” <i>Letters in Mathematical Physics</i>, vol. 111. Springer Nature, 2021.","mla":"Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in Mathematical Physics</i>, vol. 111, 19, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11005-020-01350-5\">10.1007/s11005-020-01350-5</a>.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical Physics 111 (2021).","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11005-020-01350-5\">https://doi.org/10.1007/s11005-020-01350-5</a>.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19.","apa":"Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2021). Persistence of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01350-5\">https://doi.org/10.1007/s11005-020-01350-5</a>","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical Physics</i>. 2021;111. doi:<a href=\"https://doi.org/10.1007/s11005-020-01350-5\">10.1007/s11005-020-01350-5</a>"},"oa":1,"acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged. Open Access funding provided by Institute of Science and Technology (IST Austria)","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"volume":111,"month":"02","scopus_import":"1","file_date_updated":"2021-03-09T11:44:34Z","oa_version":"Published Version","_id":"9225","article_number":"19","file":[{"date_created":"2021-03-09T11:44:34Z","success":1,"content_type":"application/pdf","relation":"main_file","file_size":391205,"file_name":"2021_LettersMathPhysics_Feliciangeli.pdf","file_id":"9232","creator":"dernst","access_level":"open_access","date_updated":"2021-03-09T11:44:34Z","checksum":"ffbfe1aad623bce7ff529c207e343b53"}],"doi":"10.1007/s11005-020-01350-5","tmp":{"short":"CC BY (4.0)","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)"},"external_id":{"isi":["000617195700001"]},"date_updated":"2026-04-08T06:59:49Z","related_material":{"record":[{"relation":"dissertation_contains","id":"9733","status":"public"}]},"department":[{"_id":"RoSe"}],"status":"public","date_published":"2021-02-11T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2021-03-07T23:01:25Z","article_type":"original","type":"journal_article","publisher":"Springer Nature","ddc":["510"],"year":"2021","license":"https://creativecommons.org/licenses/by/4.0/"},{"article_type":"original","type":"journal_article","publisher":"Springer Nature","ddc":["510"],"pmid":1,"year":"2021","status":"public","date_published":"2021-02-26T00:00:00Z","date_created":"2021-03-14T23:01:34Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000622226200001"],"arxiv":["2001.03993"],"pmid":["33785964"]},"date_updated":"2025-06-12T06:35:22Z","department":[{"_id":"RoSe"}],"file_date_updated":"2021-03-22T08:31:29Z","oa_version":"Published Version","file":[{"date_updated":"2021-03-22T08:31:29Z","access_level":"open_access","checksum":"23449e44dc5132501a5c86e70638800f","file_id":"9270","file_name":"2021_ArchRationalMechAnal_Leopold.pdf","file_size":558006,"creator":"dernst","relation":"main_file","content_type":"application/pdf","success":1,"date_created":"2021-03-22T08:31:29Z"}],"_id":"9246","tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.1007/s00205-021-01616-9","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"volume":240,"scopus_import":"1","month":"02","author":[{"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":"Mitrouskas, David Johannes","last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"}],"language":[{"iso":"eng"}],"page":"383-417","citation":{"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.","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>.","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>","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>","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417.","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>.","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."},"isi":1,"article_processing_charge":"No","oa":1,"arxiv":1,"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.","day":"26","quality_controlled":"1","publication":"Archive for Rational Mechanics and Analysis","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."}],"intvolume":"       240","has_accepted_license":"1","publication_status":"published","title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","ec_funded":1},{"day":"09","quality_controlled":"1","publication":"Letters in Mathematical Physics","abstract":[{"text":"We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.","lang":"eng"}],"intvolume":"       111","has_accepted_license":"1","title":"Free energy asymptotics of the quantum Heisenberg spin chain","publication_status":"published","volume":111,"scopus_import":"1","month":"03","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"oa":1,"acknowledgement":"The work of MN was supported by the National Science Centre (NCN) Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","author":[{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M","last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","isi":1,"citation":{"ista":"Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31.","chicago":"Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics of the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11005-021-01375-4\">https://doi.org/10.1007/s11005-021-01375-4</a>.","ama":"Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg spin chain. <i>Letters in Mathematical Physics</i>. 2021;111(2). doi:<a href=\"https://doi.org/10.1007/s11005-021-01375-4\">10.1007/s11005-021-01375-4</a>","apa":"Napiórkowski, M. M., &#38; Seiringer, R. (2021). Free energy asymptotics of the quantum Heisenberg spin chain. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01375-4\">https://doi.org/10.1007/s11005-021-01375-4</a>","short":"M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021).","mla":"Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of the Quantum Heisenberg Spin Chain.” <i>Letters in Mathematical Physics</i>, vol. 111, no. 2, 31, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11005-021-01375-4\">10.1007/s11005-021-01375-4</a>.","ieee":"M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum Heisenberg spin chain,” <i>Letters in Mathematical Physics</i>, vol. 111, no. 2. Springer Nature, 2021."},"department":[{"_id":"RoSe"}],"external_id":{"pmid":["33785980"],"isi":["000626837400001"]},"date_updated":"2026-04-02T14:06:48Z","doi":"10.1007/s11005-021-01375-4","tmp":{"short":"CC BY (4.0)","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)"},"file_date_updated":"2021-03-22T11:01:09Z","oa_version":"Published Version","_id":"9256","file":[{"date_updated":"2021-03-22T11:01:09Z","access_level":"open_access","checksum":"687fef1525789c0950de90468dd81604","file_id":"9273","file_name":"2021_LettersMathPhysics_Napiorkowski.pdf","file_size":397962,"creator":"dernst","relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2021-03-22T11:01:09Z"}],"article_number":"31","ddc":["510"],"pmid":1,"issue":"2","year":"2021","type":"journal_article","article_type":"original","publisher":"Springer Nature","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2021-03-21T23:01:19Z","status":"public","date_published":"2021-03-09T00:00:00Z"},{"oa":1,"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).","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","last_name":"Bossmann"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","last_name":"Petrat","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"article_processing_charge":"Yes (via OA deal)","citation":{"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.","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>.","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","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>","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>","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.","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>."},"isi":1,"month":"03","scopus_import":"1","volume":9,"publication_identifier":{"eissn":["2050-5094"]},"ec_funded":1,"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"}],"intvolume":"         9","publication":"Forum of Mathematics, Sigma","title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","publication_status":"published","has_accepted_license":"1","day":"26","quality_controlled":"1","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2021-04-11T22:01:15Z","date_published":"2021-03-26T00:00:00Z","status":"public","ddc":["510"],"year":"2021","publisher":"Cambridge University Press","article_type":"original","type":"journal_article","doi":"10.1017/fms.2021.22","tmp":{"short":"CC BY (4.0)","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)"},"oa_version":"Published Version","file_date_updated":"2021-04-12T07:15:58Z","file":[{"content_type":"application/pdf","success":1,"date_created":"2021-04-12T07:15:58Z","relation":"main_file","file_id":"9319","file_size":883851,"file_name":"2021_ForumMath_Bossmann.pdf","creator":"dernst","date_updated":"2021-04-12T07:15:58Z","access_level":"open_access","checksum":"17a3e6786d1e930cf0c14a880a6d7e92"}],"_id":"9318","article_number":"e28","department":[{"_id":"RoSe"}],"external_id":{"isi":["000634006900001"]},"date_updated":"2026-04-02T14:02:29Z"},{"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2021-04-18T22:01:41Z","date_published":"2021-04-05T00:00:00Z","status":"public","ddc":["510"],"year":"2021","publisher":"Springer Nature","article_type":"original","type":"journal_article","doi":"10.1007/s11005-021-01380-7","tmp":{"short":"CC BY (4.0)","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)"},"oa_version":"Published Version","file_date_updated":"2021-04-19T10:40:01Z","article_number":"45","_id":"9333","file":[{"access_level":"open_access","date_updated":"2021-04-19T10:40:01Z","checksum":"be56c0845a43c0c5c772ee0b5053f7d7","file_size":438084,"file_name":"2021_LettersMathPhysics_Mitrouskas.pdf","file_id":"9341","creator":"dernst","relation":"main_file","date_created":"2021-04-19T10:40:01Z","success":1,"content_type":"application/pdf"}],"department":[{"_id":"RoSe"}],"external_id":{"isi":["000637359300002"]},"date_updated":"2026-04-02T13:58:00Z","oa":1,"acknowledgement":"I thank Marcel Griesemer for many interesting discussions about the Fröhlich polaron and also for valuable comments on this manuscript. Helpful discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged. This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems. Open Access funding enabled and organized by Projekt DEAL.","language":[{"iso":"eng"}],"author":[{"first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes"}],"article_processing_charge":"No","citation":{"apa":"Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling limit. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01380-7\">https://doi.org/10.1007/s11005-021-01380-7</a>","ama":"Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit. <i>Letters in Mathematical Physics</i>. 2021;111. doi:<a href=\"https://doi.org/10.1007/s11005-021-01380-7\">10.1007/s11005-021-01380-7</a>","chicago":"Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11005-021-01380-7\">https://doi.org/10.1007/s11005-021-01380-7</a>.","ista":"Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 111, 45.","short":"D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021).","mla":"Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” <i>Letters in Mathematical Physics</i>, vol. 111, 45, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11005-021-01380-7\">10.1007/s11005-021-01380-7</a>.","ieee":"D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling limit,” <i>Letters in Mathematical Physics</i>, vol. 111. Springer Nature, 2021."},"isi":1,"month":"04","scopus_import":"1","volume":111,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"intvolume":"       111","abstract":[{"text":"We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.","lang":"eng"}],"publication":"Letters in Mathematical Physics","title":"A note on the Fröhlich dynamics in the strong coupling limit","publication_status":"published","has_accepted_license":"1","day":"05","quality_controlled":"1"},{"external_id":{"isi":["000644702800005"],"arxiv":["1911.03187"]},"date_updated":"2023-08-08T13:15:11Z","department":[{"_id":"RoSe"}],"oa_version":"Preprint","_id":"9348","article_number":"109029","doi":"10.1016/j.jfa.2021.109029","publisher":"Elsevier","article_type":"original","type":"journal_article","issue":"3","year":"2021","date_published":"2021-04-07T00:00:00Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2021-04-25T22:01:29Z","day":"07","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1911.03187"}],"abstract":[{"lang":"eng","text":"We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension."}],"intvolume":"       281","publication":"Journal of Functional Analysis","title":"Sharp tunneling estimates for a double-well model in infinite dimension","publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"month":"04","scopus_import":"1","volume":281,"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-6249-0928","full_name":"Brooks, Morris","last_name":"Brooks","first_name":"Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425"},{"first_name":"Giacomo","last_name":"Di Gesù","full_name":"Di Gesù, Giacomo"}],"isi":1,"citation":{"short":"M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021).","ista":"Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 281(3), 109029.","chicago":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>.","apa":"Brooks, M., &#38; Di Gesù, G. (2021). Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>","ama":"Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. 2021;281(3). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>","ieee":"M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model in infinite dimension,” <i>Journal of Functional Analysis</i>, vol. 281, no. 3. Elsevier, 2021.","mla":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>, vol. 281, no. 3, 109029, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>."},"article_processing_charge":"No","oa":1,"acknowledgement":"GDG gratefully acknowledges the financial support of HIM Bonn in the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness, PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La Sapienza during his frequent visits.","arxiv":1},{"quality_controlled":"1","day":"08","has_accepted_license":"1","title":"A large deviation principle in many-body quantum dynamics","publication_status":"published","publication":"Annales Henri Poincare","abstract":[{"lang":"eng","text":"We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years. "}],"intvolume":"        22","ec_funded":1,"publication_identifier":{"issn":["1424-0637"]},"volume":22,"scopus_import":"1","month":"04","page":"2595-2618","article_processing_charge":"Yes (via OA deal)","isi":1,"citation":{"ieee":"K. Kirkpatrick, S. A. E. Rademacher, and B. Schlein, “A large deviation principle in many-body quantum dynamics,” <i>Annales Henri Poincare</i>, vol. 22. Springer Nature, pp. 2595–2618, 2021.","mla":"Kirkpatrick, Kay, et al. “A Large Deviation Principle in Many-Body Quantum Dynamics.” <i>Annales Henri Poincare</i>, vol. 22, Springer Nature, 2021, pp. 2595–618, doi:<a href=\"https://doi.org/10.1007/s00023-021-01044-1\">10.1007/s00023-021-01044-1</a>.","short":"K. Kirkpatrick, S.A.E. Rademacher, B. Schlein, Annales Henri Poincare 22 (2021) 2595–2618.","ista":"Kirkpatrick K, Rademacher SAE, Schlein B. 2021. A large deviation principle in many-body quantum dynamics. Annales Henri Poincare. 22, 2595–2618.","chicago":"Kirkpatrick, Kay, Simone Anna Elvira Rademacher, and Benjamin Schlein. “A Large Deviation Principle in Many-Body Quantum Dynamics.” <i>Annales Henri Poincare</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01044-1\">https://doi.org/10.1007/s00023-021-01044-1</a>.","apa":"Kirkpatrick, K., Rademacher, S. A. E., &#38; Schlein, B. (2021). A large deviation principle in many-body quantum dynamics. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01044-1\">https://doi.org/10.1007/s00023-021-01044-1</a>","ama":"Kirkpatrick K, Rademacher SAE, Schlein B. A large deviation principle in many-body quantum dynamics. <i>Annales Henri Poincare</i>. 2021;22:2595-2618. doi:<a href=\"https://doi.org/10.1007/s00023-021-01044-1\">10.1007/s00023-021-01044-1</a>"},"author":[{"full_name":"Kirkpatrick, Kay","first_name":"Kay","last_name":"Kirkpatrick"},{"orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","last_name":"Rademacher","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"}],"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"language":[{"iso":"eng"}],"arxiv":1,"acknowledgement":"The authors gratefully acknowledge Gérard Ben Arous for suggesting this kind of result. K.L.K. was partially supported by NSF CAREER Award DMS-125479 and a Simons Sabbatical Fellowship. S.R. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. B. S. gratefully acknowledges partial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose–Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS. Funding Open access funding provided by Institute of Science and Technology (IST Austria).","oa":1,"date_updated":"2025-06-12T06:39:59Z","external_id":{"isi":["000638022600001"],"arxiv":["2010.13754"],"pmid":["34776771"]},"department":[{"_id":"RoSe"}],"_id":"9351","file":[{"relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2021-10-15T11:15:40Z","checksum":"1a0fb963f2f415ba470881a794f20eb6","date_updated":"2021-10-15T11:15:40Z","access_level":"open_access","creator":"cchlebak","file_id":"10143","file_name":"2021_Annales_Kirkpatrick.pdf","file_size":522669}],"file_date_updated":"2021-10-15T11:15:40Z","oa_version":"Published Version","doi":"10.1007/s00023-021-01044-1","tmp":{"short":"CC BY (4.0)","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)"},"type":"journal_article","article_type":"original","publisher":"Springer Nature","year":"2021","ddc":["530"],"pmid":1,"status":"public","date_published":"2021-04-08T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-04-25T22:01:30Z"},{"issue":"6","year":"2021","publisher":"Elsevier","type":"journal_article","article_type":"original","date_created":"2021-06-06T22:01:28Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2021-09-15T00:00:00Z","status":"public","department":[{"_id":"RoSe"}],"external_id":{"arxiv":["2009.00992"],"isi":["000656508600008"]},"date_updated":"2025-04-14T07:26:53Z","doi":"10.1016/j.jfa.2021.109096","oa_version":"Preprint","article_number":"109096","_id":"9462","scopus_import":"1","month":"09","volume":281,"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"oa":1,"acknowledgement":"Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.","arxiv":1,"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"author":[{"full_name":"Deuchert, Andreas","last_name":"Deuchert","first_name":"Andreas"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"isi":1,"article_processing_charge":"No","citation":{"short":"A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021).","apa":"Deuchert, A., &#38; Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>","ama":"Deuchert A, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. 2021;281(6). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>","ista":"Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>.","mla":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>, vol. 281, no. 6, 109096, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>.","ieee":"A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons,” <i>Journal of Functional Analysis</i>, vol. 281, no. 6. Elsevier, 2021."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.00992"}],"day":"15","quality_controlled":"1","ec_funded":1,"intvolume":"       281","abstract":[{"lang":"eng","text":"We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions."}],"publication":"Journal of Functional Analysis","publication_status":"published","title":"Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons"},{"article_number":"2101.12566","_id":"9787","oa_version":"Preprint","tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.48550/arXiv.2101.12566","date_updated":"2026-04-08T06:59:49Z","related_material":{"record":[{"status":"public","id":"10224","relation":"later_version"},{"relation":"dissertation_contains","id":"9733","status":"public"}]},"external_id":{"arxiv":["2101.12566"]},"department":[{"_id":"RoSe"}],"date_published":"2021-02-01T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-08-06T08:25:57Z","type":"preprint","year":"2021","ddc":["510"],"title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","corr_author":"1","publication_status":"draft","has_accepted_license":"1","abstract":[{"lang":"eng","text":"We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging."}],"publication":"arXiv","ec_funded":1,"day":"01","main_file_link":[{"url":"https://arxiv.org/abs/2101.12566","open_access":"1"}],"article_processing_charge":"No","citation":{"chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2101.12566\">https://doi.org/10.48550/arXiv.2101.12566</a>.","ista":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv, 2101.12566.","apa":"Feliciangeli, D., &#38; Seiringer, R. (n.d.). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2101.12566\">https://doi.org/10.48550/arXiv.2101.12566</a>","ama":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2101.12566\">10.48550/arXiv.2101.12566</a>","short":"D. Feliciangeli, R. Seiringer, ArXiv (n.d.).","ieee":"D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” <i>arXiv</i>. .","mla":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>ArXiv</i>, 2101.12566, doi:<a href=\"https://doi.org/10.48550/arXiv.2101.12566\">10.48550/arXiv.2101.12566</a>."},"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"}],"acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. We would also like to thank Rupert Frank for many helpful discussions, especially related to the Gross coordinate transformation defined in Def. 4.1.\r\n","arxiv":1,"oa":1,"month":"02"},{"ec_funded":1,"OA_place":"repository","publication":"arXiv","abstract":[{"text":"We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar.","lang":"eng"}],"title":"The effective mass problem for the Landau-Pekar equations","publication_status":"draft","corr_author":"1","main_file_link":[{"url":"https://arxiv.org/abs/2107.03720","open_access":"1"}],"day":"08","oa":1,"arxiv":1,"acknowledgement":"We thank Herbert Spohn for helpful comments. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged..","author":[{"orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","last_name":"Rademacher","full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"citation":{"short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.).","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03720\">10.48550/arXiv.2107.03720</a>","apa":"Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (n.d.). The effective mass problem for the Landau-Pekar equations. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2107.03720\">https://doi.org/10.48550/arXiv.2107.03720</a>","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2107.03720\">https://doi.org/10.48550/arXiv.2107.03720</a>.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. arXiv, 2107.03720.","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” <i>ArXiv</i>, 2107.03720, doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03720\">10.48550/arXiv.2107.03720</a>.","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” <i>arXiv</i>. ."},"article_processing_charge":"No","month":"07","doi":"10.48550/arXiv.2107.03720","oa_version":"Preprint","article_number":"2107.03720 ","_id":"9791","department":[{"_id":"RoSe"}],"external_id":{"arxiv":["2107.03720"]},"date_updated":"2026-04-08T06:59:49Z","related_material":{"record":[{"id":"10755","relation":"later_version","status":"public"},{"relation":"dissertation_contains","id":"9733","status":"public"}]},"date_created":"2021-08-06T08:49:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2021-07-08T00:00:00Z","ddc":["510"],"year":"2021","type":"preprint"},{"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"external_id":{"arxiv":["2106.11217"]},"related_material":{"record":[{"status":"public","relation":"later_version","id":"12911"},{"status":"public","relation":"dissertation_contains","id":"9733"},{"status":"public","id":"10030","relation":"dissertation_contains"}]},"date_updated":"2026-04-08T07:00:03Z","tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.48550/arXiv.2106.11217","oa_version":"Preprint","_id":"9792","article_number":"2106.11217","ddc":["510"],"year":"2021","type":"preprint","date_created":"2021-08-06T09:07:12Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2021-07-21T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"day":"21","ec_funded":1,"publication":"arXiv","abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on careful a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem."}],"has_accepted_license":"1","publication_status":"draft","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","month":"07","oa":1,"arxiv":1,"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thanks the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. Finally, the authors also thanks J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article.  L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and NoF65. D.F acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","last_name":"Feliciangeli"},{"first_name":"Augusto","last_name":"Gerolin","full_name":"Gerolin, Augusto"},{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"citation":{"apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>.","ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, 2106.11217, doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>arXiv</i>. ."},"article_processing_charge":"No"},{"oa_version":"Published Version","file_date_updated":"2021-10-27T12:57:06Z","article_number":"083305","_id":"9891","file":[{"relation":"main_file","date_created":"2021-10-27T12:57:06Z","content_type":"application/pdf","success":1,"access_level":"open_access","date_updated":"2021-10-27T12:57:06Z","checksum":"d035be2b894c4d50d90ac5ce252e27cd","file_name":"2021_JMathPhy_Lauritsen.pdf","file_size":4352640,"file_id":"10188","creator":"cziletti"}],"doi":"10.1063/5.0053494","tmp":{"short":"CC BY (4.0)","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)"},"external_id":{"arxiv":["2103.07975"],"isi":["000683960800003"]},"date_updated":"2024-10-09T21:00:48Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"date_published":"2021-08-01T00:00:00Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2021-08-12T07:08:36Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publisher":"AIP Publishing","type":"journal_article","article_type":"original","issue":"8","ddc":["530"],"year":"2021","intvolume":"        62","abstract":[{"text":"Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.","lang":"eng"}],"publication":"Journal of Mathematical Physics","publication_status":"published","corr_author":"1","title":"Floating Wigner crystal and periodic jellium configurations","has_accepted_license":"1","day":"01","quality_controlled":"1","language":[{"iso":"eng"}],"author":[{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"citation":{"chicago":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>.","ista":"Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305.","apa":"Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>","ama":"Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. 2021;62(8). doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>","short":"A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).","mla":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>.","ieee":"A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8. AIP Publishing, 2021."},"article_processing_charge":"No","isi":1,"oa":1,"acknowledgement":"The author would like to thank Robert Seiringer for guidance and many helpful comments on this project. The author would also like to thank Mathieu Lewin for his comments on the manuscript and Lorenzo Portinale for providing his lecture notes for the course “Mathematics of quantum many-body systems” in spring 2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these lecture notes.","arxiv":1,"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"scopus_import":"1","month":"08","volume":62},{"month":"08","publication_identifier":{"issn":["2663-337X"]},"oa":1,"page":"180","article_processing_charge":"No","citation":{"ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","mla":"Feliciangeli, Dario. <i>The Polaron at Strong Coupling</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>.","apa":"Feliciangeli, D. (2021). <i>The polaron at strong coupling</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021."},"author":[{"orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"}],"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"language":[{"iso":"eng"}],"degree_awarded":"PhD","day":"20","ec_funded":1,"has_accepted_license":"1","corr_author":"1","publication_status":"published","title":"The polaron at strong coupling","OA_place":"publisher","abstract":[{"text":"This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.","lang":"eng"}],"year":"2021","license":"https://creativecommons.org/licenses/by-nd/4.0/","ddc":["515","519","539"],"type":"dissertation","publisher":"Institute of Science and Technology Austria","date_created":"2021-07-27T15:48:30Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","status":"public","date_published":"2021-08-20T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"9787","status":"public"},{"id":"9792","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"9791","status":"public"},{"relation":"part_of_dissertation","id":"9225","status":"public"},{"relation":"part_of_dissertation","id":"9781","status":"public"}]},"date_updated":"2026-07-06T14:02:25Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)"},"doi":"10.15479/at:ista:9733","supervisor":[{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas"}],"alternative_title":["ISTA Thesis"],"_id":"9733","file":[{"relation":"main_file","date_created":"2021-08-19T14:03:48Z","content_type":"application/pdf","access_level":"open_access","date_updated":"2021-09-06T09:28:56Z","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_name":"Thesis_FeliciangeliA.pdf","file_size":1958710,"file_id":"9944","creator":"dfelicia"},{"creator":"dfelicia","file_id":"9945","file_size":3771669,"file_name":"thesis.7z","checksum":"72810843abee83705853505b3f8348aa","date_updated":"2022-03-10T12:13:57Z","access_level":"closed","content_type":"application/octet-stream","date_created":"2021-08-19T14:06:35Z","relation":"source_file"}],"file_date_updated":"2022-03-10T12:13:57Z","oa_version":"Published Version"},{"day":"01","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1903.04046","open_access":"1"}],"publication":"Pure and Applied Analysis","abstract":[{"lang":"eng","text":"We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space."}],"intvolume":"         2","title":" The local density approximation in density functional theory","publication_status":"published","corr_author":"1","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"volume":2,"month":"01","scopus_import":"1","author":[{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"last_name":"Lieb","first_name":"Elliott H.","full_name":"Lieb, Elliott H."},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"language":[{"iso":"eng"}],"page":"35-73","citation":{"mla":"Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>, vol. 2, no. 1, Mathematical Sciences Publishers, 2020, pp. 35–73, doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>.","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation in density functional theory,” <i>Pure and Applied Analysis</i>, vol. 2, no. 1. Mathematical Sciences Publishers, pp. 35–73, 2020.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.","ama":"Lewin M, Lieb EH, Seiringer R.  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. 2020;2(1):35-73. doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2020).  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>.","ista":"Lewin M, Lieb EH, Seiringer R. 2020.  The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73."},"article_processing_charge":"No","oa":1,"arxiv":1,"external_id":{"arxiv":["1903.04046"]},"date_updated":"2024-10-09T21:08:02Z","department":[{"_id":"RoSe"}],"oa_version":"Preprint","_id":"14891","doi":"10.2140/paa.2020.2.35","type":"journal_article","article_type":"original","publisher":"Mathematical Sciences Publishers","issue":"1","year":"2020","status":"public","date_published":"2020-01-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-01-28T23:01:44Z"},{"date_updated":"2025-04-14T07:44:03Z","external_id":{"isi":["000551556000006"]},"department":[{"_id":"RoSe"}],"file":[{"content_type":"application/pdf","success":1,"date_created":"2020-11-20T12:04:26Z","relation":"main_file","creator":"dernst","file_id":"8784","file_name":"2020_LettersMathPhysics_Rademacher.pdf","file_size":478683,"checksum":"3bdd41f10ad947b67a45b98f507a7d4a","date_updated":"2020-11-20T12:04:26Z","access_level":"open_access"}],"_id":"7611","oa_version":"Published Version","file_date_updated":"2020-11-20T12:04:26Z","tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.1007/s11005-020-01286-w","publisher":"Springer Nature","article_type":"original","type":"journal_article","year":"2020","ddc":["510"],"date_published":"2020-03-12T00:00:00Z","status":"public","date_created":"2020-03-23T11:11:47Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","day":"12","publication_status":"published","corr_author":"1","title":"Central limit theorem for Bose gases interacting through singular potentials","has_accepted_license":"1","intvolume":"       110","abstract":[{"text":"We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.","lang":"eng"}],"publication":"Letters in Mathematical Physics","ec_funded":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"month":"03","scopus_import":"1","volume":110,"citation":{"mla":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” <i>Letters in Mathematical Physics</i>, vol. 110, Springer Nature, 2020, pp. 2143–74, doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>.","ieee":"S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through singular potentials,” <i>Letters in Mathematical Physics</i>, vol. 110. Springer Nature, pp. 2143–2174, 2020.","ista":"Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. 110, 2143–2174.","chicago":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>.","apa":"Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>","ama":"Rademacher SAE. Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>","short":"S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174."},"isi":1,"article_processing_charge":"Yes (via OA deal)","page":"2143-2174","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"author":[{"last_name":"Rademacher","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira"}],"acknowledgement":"Simone Rademacher acknowledges partial support from the NCCR SwissMAP. This project has received\r\nfunding from the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R. would like to thank Benjamin Schlein for many fruitful discussions.","oa":1},{"tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.1007/s00205-020-01489-4","oa_version":"Published Version","file_date_updated":"2020-11-20T13:17:42Z","_id":"7650","file":[{"relation":"main_file","content_type":"application/pdf","success":1,"date_created":"2020-11-20T13:17:42Z","checksum":"b645fb64bfe95bbc05b3eea374109a9c","date_updated":"2020-11-20T13:17:42Z","access_level":"open_access","creator":"dernst","file_id":"8785","file_size":704633,"file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf"}],"department":[{"_id":"RoSe"}],"external_id":{"arxiv":["1901.11363"],"isi":["000519415000001"]},"date_updated":"2025-04-14T07:27:00Z","date_created":"2020-04-08T15:18:03Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_published":"2020-03-09T00:00:00Z","status":"public","issue":"6","ddc":["510"],"year":"2020","publisher":"Springer Nature","type":"journal_article","article_type":"original","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution."}],"intvolume":"       236","publication":"Archive for Rational Mechanics and Analysis","title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","corr_author":"1","publication_status":"published","has_accepted_license":"1","day":"09","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions. Financial support by the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (Grant Agreement No. 694227) is gratefully acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 836146.","arxiv":1,"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas","last_name":"Deuchert","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"article_processing_charge":"Yes (via OA deal)","citation":{"short":"A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 1217–1271.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>.","ista":"Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6), 1217–1271.","ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271. doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>","apa":"Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>","mla":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>.","ieee":"A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020."},"isi":1,"page":"1217-1271","month":"03","scopus_import":"1","volume":236,"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]}},{"article_number":"e20","_id":"7790","file":[{"checksum":"8a64da99d107686997876d7cad8cfe1e","access_level":"open_access","date_updated":"2020-07-14T12:48:03Z","creator":"dernst","file_name":"2020_ForumMath_Deuchert.pdf","file_size":692530,"file_id":"7797","relation":"main_file","date_created":"2020-05-04T12:02:41Z","content_type":"application/pdf"}],"oa_version":"Published Version","file_date_updated":"2020-07-14T12:48:03Z","tmp":{"short":"CC BY (4.0)","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)"},"doi":"10.1017/fms.2020.17","related_material":{"record":[{"status":"public","id":"7524","relation":"earlier_version"}]},"date_updated":"2026-04-03T09:30:21Z","external_id":{"isi":["000527342000001"],"arxiv":["1910.03372"]},"department":[{"_id":"RoSe"}],"date_published":"2020-03-14T00:00:00Z","status":"public","date_created":"2020-05-03T22:00:48Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Cambridge University Press","article_type":"original","type":"journal_article","year":"2020","ddc":["510"],"publication_status":"published","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","corr_author":"1","has_accepted_license":"1","intvolume":"         8","abstract":[{"lang":"eng","text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 ."}],"publication":"Forum of Mathematics, Sigma","ec_funded":1,"quality_controlled":"1","day":"14","isi":1,"article_processing_charge":"No","citation":{"ista":"Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>","short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020."},"language":[{"iso":"eng"}],"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"author":[{"orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas","last_name":"Deuchert","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mayer, Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","first_name":"Simon"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"arxiv":1,"oa":1,"publication_identifier":{"eissn":["2050-5094"]},"month":"03","scopus_import":"1","volume":8},{"page":"448-464","article_processing_charge":"Yes (via OA deal)","citation":{"short":"R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.","ama":"Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. 2020;181:448-464. doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>","apa":"Seiringer, R., &#38; Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>","ista":"Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464.","chicago":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>.","ieee":"R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” <i>Journal of Statistical Physics</i>, vol. 181. Springer, pp. 448–464, 2020.","mla":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>, vol. 181, Springer, 2020, pp. 448–64, doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>."},"isi":1,"author":[{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"language":[{"iso":"eng"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"arxiv":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\nThe work of R.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. ","oa":1,"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"volume":181,"month":"10","scopus_import":"1","has_accepted_license":"1","title":"Emergence of Haldane pseudo-potentials in systems with short-range interactions","publication_status":"published","corr_author":"1","publication":"Journal of Statistical Physics","abstract":[{"lang":"eng","text":"In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level."}],"intvolume":"       181","ec_funded":1,"quality_controlled":"1","day":"01","status":"public","date_published":"2020-10-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-07-05T22:00:46Z","type":"journal_article","article_type":"original","publisher":"Springer","year":"2020","ddc":["530"],"file":[{"content_type":"application/pdf","success":1,"date_created":"2020-11-25T15:05:04Z","relation":"main_file","creator":"dernst","file_id":"8812","file_name":"2020_JourStatPhysics_Seiringer.pdf","file_size":404778,"checksum":"5cbeef52caf18d0d952f17fed7b5545a","date_updated":"2020-11-25T15:05:04Z","access_level":"open_access"}],"_id":"8091","file_date_updated":"2020-11-25T15:05:04Z","oa_version":"Published Version","doi":"10.1007/s10955-020-02586-0","tmp":{"short":"CC BY (4.0)","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)"},"date_updated":"2025-07-10T11:55:04Z","external_id":{"isi":["000543030000002"],"arxiv":["2001.07144"]},"department":[{"_id":"RoSe"}]},{"external_id":{"isi":["000550164400001"],"arxiv":["1907.04547"]},"date_updated":"2025-04-14T07:44:05Z","department":[{"_id":"RoSe"}],"oa_version":"Published Version","file_date_updated":"2020-12-02T08:50:38Z","_id":"8130","file":[{"success":1,"content_type":"application/pdf","date_created":"2020-12-02T08:50:38Z","relation":"main_file","file_id":"8826","file_size":942343,"file_name":"2020_ArchiveRatMech_Bossmann.pdf","creator":"dernst","date_updated":"2020-12-02T08:50:38Z","access_level":"open_access","checksum":"cc67a79a67bef441625fcb1cd031db3d"}],"doi":"10.1007/s00205-020-01548-w","tmp":{"short":"CC BY (4.0)","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)"},"publisher":"Springer Nature","article_type":"original","type":"journal_article","issue":"11","ddc":["510"],"year":"2020","date_published":"2020-11-01T00:00:00Z","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2020-07-18T15:06:35Z","day":"01","quality_controlled":"1","abstract":[{"lang":"eng","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."}],"intvolume":"       238","publication":"Archive for Rational Mechanics and Analysis","publication_status":"published","title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","corr_author":"1","has_accepted_license":"1","ec_funded":1,"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"month":"11","scopus_import":"1","volume":238,"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"language":[{"iso":"eng"}],"author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann"}],"isi":1,"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>.","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.","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>","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","ieee":"L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020.","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>."},"article_processing_charge":"Yes (via OA deal)","page":"541-606","oa":1,"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.","arxiv":1},{"publication_identifier":{"issn":["0022-2488"]},"scopus_import":"1","month":"06","volume":61,"project":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"author":[{"full_name":"Mayer, Simon","first_name":"Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"article_processing_charge":"No","isi":1,"citation":{"short":"S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).","chicago":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>.","ista":"Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.","ama":"Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>","apa":"Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>","mla":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6, 061901, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>.","ieee":"S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6. AIP Publishing, 2020."},"oa":1,"arxiv":1,"day":"22","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/2002.08281","open_access":"1"}],"abstract":[{"lang":"eng","text":"We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion."}],"intvolume":"        61","publication":"Journal of Mathematical Physics","corr_author":"1","title":"The free energy of the two-dimensional dilute Bose gas. II. Upper bound","publication_status":"published","ec_funded":1,"publisher":"AIP Publishing","type":"journal_article","article_type":"original","issue":"6","year":"2020","date_published":"2020-06-22T00:00:00Z","status":"public","date_created":"2020-07-19T22:00:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000544595100001"],"arxiv":["2002.08281"]},"date_updated":"2025-07-10T11:55:05Z","department":[{"_id":"RoSe"}],"oa_version":"Preprint","_id":"8134","article_number":"061901","doi":"10.1063/5.0005950"}]