[{"date_updated":"2023-11-14T13:21:01Z","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"_id":"12911","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"ec_funded":1,"issue":"4","related_material":{"record":[{"id":"9792","status":"public","relation":"earlier_version"}]},"volume":285,"oa_version":"Preprint","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 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."}],"intvolume":" 285","month":"08","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963","apa":"Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963."},"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","article_processing_charge":"No","external_id":{"isi":["000990804300001"],"arxiv":["2106.11217"]},"author":[{"last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"first_name":"Augusto","last_name":"Gerolin","full_name":"Gerolin, Augusto"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"article_number":"109963","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"publication":"Journal of Functional Analysis","day":"15","year":"2023","isi":1,"date_created":"2023-05-07T22:01:02Z","date_published":"2023-08-15T00:00:00Z","doi":"10.1016/j.jfa.2023.109963","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 thank 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. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.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 HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","oa":1,"publisher":"Elsevier","quality_controlled":"1"},{"publication":"Journal of Physics A: Mathematical and Theoretical","day":"19","year":"2022","has_accepted_license":"1","date_created":"2022-02-13T23:01:35Z","date_published":"2022-01-19T00:00:00Z","doi":"10.1088/1751-8121/ac3947","acknowledgement":"We thank Herbert Spohn for helpful comments. Funding from the European Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (SR) is\r\ngratefully acknowledged.","oa":1,"publisher":"IOP Publishing","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 55(1), 015201.","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 2022;55(1). doi:10.1088/1751-8121/ac3947","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022)."},"title":"The effective mass problem for the Landau-Pekar equations","external_id":{"arxiv":["2107.03720"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli"},{"full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","last_name":"Rademacher","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"article_number":"015201","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2022-02-14T08:20:19Z","file_size":1132380,"date_created":"2022-02-14T08:20:19Z","file_name":"2022_JournalPhysicsA_Feliciangeli.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"0875e562705563053d6dd98fba4d8578","file_id":"10757","success":1}],"publication_status":"published","publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"volume":55,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9791"}]},"issue":"1","oa_version":"Published Version","abstract":[{"text":"We provide a definition of the effective mass for the classical polaron described by the Landau–Pekar (LP) 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 LP (1948 J. Exp. Theor. Phys. 18 419–423).","lang":"eng"}],"intvolume":" 55","month":"01","scopus_import":"1","ddc":["510"],"date_updated":"2024-03-06T12:30:44Z","department":[{"_id":"RoSe"}],"file_date_updated":"2022-02-14T08:20:19Z","_id":"10755","status":"public","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","type":"journal_article"},{"quality_controlled":"1","publisher":"Springer Nature","oa":1,"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. 4.7.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","date_published":"2021-10-25T00:00:00Z","doi":"10.1007/s00205-021-01715-7","date_created":"2021-11-07T23:01:26Z","page":"1835–1906","day":"25","publication":"Archive for Rational Mechanics and Analysis","has_accepted_license":"1","isi":1,"year":"2021","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000710850600001"],"arxiv":["2101.12566"]},"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 242(3), 1835–1906.","chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01715-7.","ieee":"D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” Archive for Rational Mechanics and Analysis, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.","short":"D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906.","apa":"Feliciangeli, D., & Seiringer, R. (2021). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 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Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging.","lang":"eng"}],"issue":"3","related_material":{"record":[{"id":"9787","status":"public","relation":"earlier_version"}]},"volume":242,"ec_funded":1,"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"10544","checksum":"672e9c21b20f1a50854b7c821edbb92f","creator":"alisjak","file_size":990529,"date_updated":"2021-12-14T08:35:42Z","file_name":"2021_Springer_Feliciangeli.pdf","date_created":"2021-12-14T08:35:42Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","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)"},"_id":"10224","department":[{"_id":"RoSe"}],"file_date_updated":"2021-12-14T08:35:42Z","ddc":["530"],"date_updated":"2023-08-14T10:32:19Z"},{"oa":1,"publisher":"Springer Nature","quality_controlled":"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)","date_created":"2021-03-07T23:01:25Z","date_published":"2021-02-11T00:00:00Z","doi":"10.1007/s11005-020-01350-5","publication":"Letters in Mathematical Physics","day":"11","year":"2021","has_accepted_license":"1","isi":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_number":"19","title":"Persistence of the spectral gap for the Landau–Pekar equations","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000617195700001"]},"author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","last_name":"Rademacher"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics, vol. 111, 19, Springer Nature, 2021, doi:10.1007/s11005-020-01350-5.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical Physics 111 (2021).","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the spectral gap for the Landau–Pekar equations,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-020-01350-5","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2021). Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01350-5","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-020-01350-5.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19."},"intvolume":" 111","month":"02","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9733"}]},"volume":111,"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2021-03-09T11:44:34Z","file_size":391205,"date_created":"2021-03-09T11:44:34Z","file_name":"2021_LettersMathPhysics_Feliciangeli.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9232","checksum":"ffbfe1aad623bce7ff529c207e343b53","success":1}],"publication_status":"published","publication_identifier":{"issn":["03779017"],"eissn":["15730530"]},"status":"public","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)"},"type":"journal_article","article_type":"original","_id":"9225","file_date_updated":"2021-03-09T11:44:34Z","department":[{"_id":"RoSe"}],"ddc":["510"],"date_updated":"2023-09-07T13:30:11Z"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.12566"}],"month":"02","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."}],"oa_version":"Preprint","ec_funded":1,"related_material":{"record":[{"relation":"later_version","status":"public","id":"10224"},{"relation":"dissertation_contains","status":"public","id":"9733"}]},"publication_status":"submitted","language":[{"iso":"eng"}],"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)"},"type":"preprint","status":"public","_id":"9787","department":[{"_id":"RoSe"}],"date_updated":"2023-09-07T13:30:10Z","ddc":["510"],"oa":1,"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","date_created":"2021-08-06T08:25:57Z","date_published":"2021-02-01T00:00:00Z","year":"2021","has_accepted_license":"1","publication":"arXiv","day":"01","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"article_number":"2101.12566","article_processing_charge":"No","external_id":{"arxiv":["2101.12566"]},"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","citation":{"ista":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv, 2101.12566.","chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.","ama":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv.","apa":"Feliciangeli, D., & Seiringer, R. (n.d.). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv.","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,” arXiv. .","mla":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, 2101.12566."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425"},{"related_material":{"record":[{"status":"public","id":"9733","relation":"dissertation_contains"},{"id":"10030","status":"public","relation":"dissertation_contains"},{"relation":"later_version","status":"public","id":"12911"}]},"ec_funded":1,"publication_status":"submitted","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"month":"07","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_updated":"2023-11-14T13:21:01Z","ddc":["510"],"type":"preprint","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)"},"status":"public","_id":"9792","doi":"10.48550/arXiv.2106.11217","date_published":"2021-07-21T00:00:00Z","date_created":"2021-08-06T09:07:12Z","has_accepted_license":"1","year":"2021","day":"21","publication":"arXiv","oa":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":[{"orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"last_name":"Gerolin","full_name":"Gerolin, Augusto","first_name":"Augusto"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"article_processing_charge":"No","external_id":{"arxiv":["2106.11217"]},"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","citation":{"ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv. doi:10.48550/arXiv.2106.11217","apa":"Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv. https://doi.org/10.48550/arXiv.2106.11217","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. .","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.” ArXiv, 2106.11217, doi:10.48550/arXiv.2106.11217."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"article_number":"2106.11217"},{"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","mla":"Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","apa":"Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733"},"title":"The polaron at strong coupling","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"}],"article_processing_charge":"No","publisher":"Institute of Science and Technology Austria","oa":1,"day":"20","has_accepted_license":"1","year":"2021","date_published":"2021-08-20T00:00:00Z","doi":"10.15479/at:ista:9733","date_created":"2021-07-27T15:48:30Z","page":"180","_id":"9733","status":"public","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"ddc":["515","519","539"],"supervisor":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2024-03-06T12:30:44Z","file_date_updated":"2022-03-10T12:13:57Z","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"month":"08","alternative_title":["ISTA Thesis"],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_id":"9944","date_updated":"2021-09-06T09:28:56Z","file_size":1958710,"creator":"dfelicia","date_created":"2021-08-19T14:03:48Z","file_name":"Thesis_FeliciangeliA.pdf"},{"checksum":"72810843abee83705853505b3f8348aa","file_id":"9945","content_type":"application/octet-stream","relation":"source_file","access_level":"closed","file_name":"thesis.7z","date_created":"2021-08-19T14:06:35Z","file_size":3771669,"date_updated":"2022-03-10T12:13:57Z","creator":"dfelicia"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","related_material":{"record":[{"id":"9787","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9792"},{"relation":"part_of_dissertation","status":"public","id":"9225"},{"status":"public","id":"9781","relation":"part_of_dissertation"},{"status":"public","id":"9791","relation":"part_of_dissertation"}]},"license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1},{"external_id":{"arxiv":["2107.03720"]},"article_processing_charge":"No","author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"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"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"title":"The effective mass problem for the Landau-Pekar equations","department":[{"_id":"RoSe"}],"date_updated":"2024-03-06T12:30:45Z","citation":{"chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d.","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.” ArXiv, 2107.03720.","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” arXiv. .","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.).","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective mass problem for the Landau-Pekar equations. arXiv.","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. arXiv."},"ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"preprint","status":"public","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"_id":"9791","article_number":"2107.03720 ","ec_funded":1,"date_created":"2021-08-06T08:49:45Z","related_material":{"record":[{"id":"10755","status":"public","relation":"later_version"},{"status":"public","id":"9733","relation":"dissertation_contains"}]},"date_published":"2021-07-08T00:00:00Z","publication_status":"submitted","year":"2021","language":[{"iso":"eng"}],"publication":"arXiv","day":"08","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2107.03720"}],"oa":1,"month":"07","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"}],"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..","oa_version":"Preprint"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.08647"}],"scopus_import":"1","intvolume":" 52","month":"02","abstract":[{"text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","related_material":{"record":[{"status":"public","id":"9733","relation":"dissertation_contains"}]},"issue":"1","volume":52,"publication_status":"published","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"language":[{"iso":"eng"}],"tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","article_type":"original","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"status":"public","_id":"9781","department":[{"_id":"RoSe"}],"date_updated":"2023-09-07T13:30:11Z","ddc":["510"],"oa":1,"quality_controlled":"1","publisher":"Society for Industrial & Applied Mathematics ","acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","page":"605-622","date_created":"2021-08-06T07:34:16Z","doi":"10.1137/19m126284x","date_published":"2020-02-12T00:00:00Z","year":"2020","isi":1,"has_accepted_license":"1","publication":"SIAM Journal on Mathematical Analysis","day":"12","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"article_processing_charge":"No","external_id":{"arxiv":["1904.08647 "],"isi":["000546967700022"]},"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","citation":{"mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis, vol. 52, no. 1, Society for Industrial & Applied Mathematics , 2020, pp. 605–22, doi:10.1137/19m126284x.","ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” SIAM Journal on Mathematical Analysis, vol. 52, no. 1. Society for Industrial & Applied Mathematics , pp. 605–622, 2020.","short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 2020;52(1):605-622. doi:10.1137/19m126284x","apa":"Feliciangeli, D., & Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics . https://doi.org/10.1137/19m126284x","chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics , 2020. https://doi.org/10.1137/19m126284x.","ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}]