[{"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","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"month":"07","publication_status":"submitted","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"9733","status":"public"},{"relation":"dissertation_contains","status":"public","id":"10030"},{"status":"public","id":"12911","relation":"later_version"}]},"ec_funded":1,"_id":"9792","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","date_updated":"2023-11-14T13:21:01Z","ddc":["510"],"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"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].","oa":1,"has_accepted_license":"1","year":"2021","day":"21","publication":"arXiv","doi":"10.48550/arXiv.2106.11217","date_published":"2021-07-21T00:00:00Z","date_created":"2021-08-06T09:07:12Z","article_number":"2106.11217","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"citation":{"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.","ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","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.","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.).","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","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Augusto","full_name":"Gerolin, Augusto","last_name":"Gerolin"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, 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"},{"quality_controlled":"1","publisher":"Mathematical Sciences Publishers","oa":1,"acknowledgement":"Financial support by the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No. 754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227 (N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.), the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel Griesemer for helpful discussions.","doi":"10.2140/paa.2021.3.653","date_published":"2021-10-01T00:00:00Z","date_created":"2024-01-28T23:01:43Z","page":"653-676","day":"01","publication":"Pure and Applied Analysis","year":"2021","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron","author":[{"last_name":"Leopold","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mitrouskas, David Johannes","last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"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"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"external_id":{"arxiv":["2005.02098"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653","ama":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653","short":"N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676.","ieee":"N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021.","mla":"Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653.","ista":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 3(4), 653–676.","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653."},"month":"10","intvolume":" 3","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2005.02098"}],"oa_version":"Preprint","abstract":[{"text":"We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.","lang":"eng"}],"issue":"4","volume":3,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"14889","department":[{"_id":"RoSe"}],"date_updated":"2024-02-05T10:02:45Z"},{"title":"Beyond Bogoliubov dynamics","author":[{"last_name":"Bossmann","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"last_name":"Petrat","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"},{"first_name":"Avy","last_name":"Soffer","full_name":"Soffer, Avy"}],"article_processing_charge":"No","external_id":{"arxiv":["1912.11004"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:10.2140/paa.2021.3.677.","ama":"Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 2021;3(4):677-726. doi:10.2140/paa.2021.3.677","apa":"Bossmann, L., Petrat, S. P., Pickl, P., & Soffer, A. (2021). Beyond Bogoliubov dynamics. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2021.3.677","short":"L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726.","ieee":"L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021.","chicago":"Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.677.","ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726."},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"doi":"10.2140/paa.2021.3.677","date_published":"2021-10-01T00:00:00Z","date_created":"2024-01-28T23:01:43Z","page":"677-726","day":"01","publication":"Pure and Applied Analysis","year":"2021","publisher":"Mathematical Sciences Publishers","quality_controlled":"1","oa":1,"acknowledgement":"We are grateful for the hospitality of Central China Normal University (CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher, Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research\r\nTraining Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk lodowska-Curie Grant Agreement No. 754411.","department":[{"_id":"RoSe"}],"date_updated":"2024-02-05T09:26:31Z","status":"public","type":"journal_article","article_type":"original","_id":"14890","volume":3,"issue":"4","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"publication_status":"published","month":"10","intvolume":" 3","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.11004"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions."}]},{"language":[{"iso":"eng"}],"file":[{"date_updated":"2021-09-06T09:28:56Z","file_size":1958710,"creator":"dfelicia","date_created":"2021-08-19T14:03:48Z","file_name":"Thesis_FeliciangeliA.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_id":"9944"},{"file_id":"9945","checksum":"72810843abee83705853505b3f8348aa","content_type":"application/octet-stream","access_level":"closed","relation":"source_file","date_created":"2021-08-19T14:06:35Z","file_name":"thesis.7z","date_updated":"2022-03-10T12:13:57Z","file_size":3771669,"creator":"dfelicia"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"9787"},{"id":"9792","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"9225","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9781"},{"relation":"part_of_dissertation","status":"public","id":"9791"}]},"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"],"ddc":["515","519","539"],"date_updated":"2024-03-06T12:30:44Z","supervisor":[{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2022-03-10T12:13:57Z","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"_id":"9733","status":"public","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)"},"type":"dissertation","day":"20","year":"2021","has_accepted_license":"1","date_created":"2021-07-27T15:48:30Z","doi":"10.15479/at:ista:9733","date_published":"2021-08-20T00:00:00Z","page":"180","oa":1,"publisher":"Institute of Science and Technology Austria","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733.","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733","apa":"Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733","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."},"title":"The polaron at strong coupling","article_processing_charge":"No","author":[{"last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"}],"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}]},{"main_file_link":[{"url":"https://arxiv.org/abs/2107.03720","open_access":"1"}],"oa":1,"month":"07","abstract":[{"lang":"eng","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."}],"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","ec_funded":1,"date_created":"2021-08-06T08:49:45Z","related_material":{"record":[{"relation":"later_version","id":"10755","status":"public"},{"relation":"dissertation_contains","id":"9733","status":"public"}]},"date_published":"2021-07-08T00:00:00Z","year":"2021","publication_status":"submitted","publication":"arXiv","language":[{"iso":"eng"}],"day":"08","type":"preprint","status":"public","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_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"}],"_id":"9791","article_number":"2107.03720 ","article_processing_charge":"No","external_id":{"arxiv":["2107.03720"]},"author":[{"last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"last_name":"Rademacher","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"title":"The effective mass problem for the Landau-Pekar equations","department":[{"_id":"RoSe"}],"date_updated":"2024-03-06T12:30:45Z","citation":{"ista":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. arXiv, 2107.03720.","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d.","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.).","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. arXiv.","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective mass problem for the Landau-Pekar equations. arXiv.","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, 2107.03720."},"ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]