--- _id: '12911' 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.' 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." article_number: '109963' article_processing_charge: No article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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. 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. 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. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '10755' abstract: - lang: eng 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). 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." article_number: '015201' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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' 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.' 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.' 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.' short: 'D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022).' date_created: 2022-02-13T23:01:35Z date_published: 2022-01-19T00:00:00Z date_updated: 2024-03-06T12:30:44Z day: '19' ddc: - '510' department: - _id: RoSe doi: 10.1088/1751-8121/ac3947 ec_funded: 1 external_id: arxiv: - '2107.03720' file: - access_level: open_access checksum: 0875e562705563053d6dd98fba4d8578 content_type: application/pdf creator: dernst date_created: 2022-02-14T08:20:19Z date_updated: 2022-02-14T08:20:19Z file_id: '10757' file_name: 2022_JournalPhysicsA_Feliciangeli.pdf file_size: 1132380 relation: main_file success: 1 file_date_updated: 2022-02-14T08:20:19Z has_accepted_license: '1' intvolume: ' 55' issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'Journal of Physics A: Mathematical and Theoretical' publication_identifier: eissn: - 1751-8121 issn: - 1751-8113 publication_status: published publisher: IOP Publishing quality_controlled: '1' related_material: record: - id: '9791' relation: earlier_version status: public scopus_import: '1' status: public title: The effective mass problem for the Landau-Pekar equations tmp: 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) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2022' ... --- _id: '10224' 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. 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)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 2021;242(3):1835–1906. doi:10.1007/s00205-021-01715-7' 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. Springer Nature. https://doi.org/10.1007/s00205-021-01715-7' 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.' 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.' mla: 'Feliciangeli, Dario, and Robert 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, 2021, pp. 1835–1906, doi:10.1007/s00205-021-01715-7.' short: D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906. date_created: 2021-11-07T23:01:26Z date_published: 2021-10-25T00:00:00Z date_updated: 2023-08-14T10:32:19Z day: '25' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00205-021-01715-7 ec_funded: 1 external_id: arxiv: - '2101.12566' isi: - '000710850600001' file: - access_level: open_access checksum: 672e9c21b20f1a50854b7c821edbb92f content_type: application/pdf creator: alisjak date_created: 2021-12-14T08:35:42Z date_updated: 2021-12-14T08:35:42Z file_id: '10544' file_name: 2021_Springer_Feliciangeli.pdf file_size: 990529 relation: main_file success: 1 file_date_updated: 2021-12-14T08:35:42Z has_accepted_license: '1' intvolume: ' 242' isi: 1 issue: '3' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1835–1906 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '9787' relation: earlier_version status: public scopus_import: '1' status: public title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics' tmp: 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) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 242 year: '2021' ... --- _id: '9225' 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." 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) article_number: '19' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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. 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. ista: Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19. 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). date_created: 2021-03-07T23:01:25Z date_published: 2021-02-11T00:00:00Z date_updated: 2023-09-07T13:30:11Z day: '11' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-020-01350-5 ec_funded: 1 external_id: isi: - '000617195700001' file: - access_level: open_access checksum: ffbfe1aad623bce7ff529c207e343b53 content_type: application/pdf creator: dernst date_created: 2021-03-09T11:44:34Z date_updated: 2021-03-09T11:44:34Z file_id: '9232' file_name: 2021_LettersMathPhysics_Feliciangeli.pdf file_size: 391205 relation: main_file success: 1 file_date_updated: 2021-03-09T11:44:34Z has_accepted_license: '1' intvolume: ' 111' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _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 publication: Letters in Mathematical Physics publication_identifier: eissn: - '15730530' issn: - '03779017' publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '9733' relation: dissertation_contains status: public scopus_import: '1' status: public title: Persistence of the spectral gap for the Landau–Pekar equations tmp: 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) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 111 year: '2021' ... --- _id: '9787' 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. 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" article_number: '2101.12566' article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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.' chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.' ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” arXiv. .' ista: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv, 2101.12566.' mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, 2101.12566.' short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.). date_created: 2021-08-06T08:25:57Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-07T13:30:10Z day: '01' ddc: - '510' department: - _id: RoSe ec_funded: 1 external_id: arxiv: - '2101.12566' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.12566 month: '02' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: arXiv publication_status: submitted related_material: record: - id: '10224' relation: later_version status: public - id: '9733' relation: dissertation_contains status: public status: public title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics' tmp: 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) short: CC BY (4.0) type: preprint user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 year: '2021' ... --- _id: '9792' 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.' 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].' article_number: '2106.11217' article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: 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 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. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. . 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. short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.). date_created: 2021-08-06T09:07:12Z date_published: 2021-07-21T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '21' ddc: - '510' department: - _id: RoSe - _id: JaMa doi: 10.48550/arXiv.2106.11217 ec_funded: 1 external_id: arxiv: - '2106.11217' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '07' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: arXiv publication_status: submitted related_material: record: - id: '9733' relation: dissertation_contains status: public - id: '10030' relation: dissertation_contains status: public - id: '12911' relation: later_version status: public status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature tmp: 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) short: CC BY (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '9733' 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. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 citation: 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. ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021. 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. date_created: 2021-07-27T15:48:30Z date_published: 2021-08-20T00:00:00Z date_updated: 2024-03-06T12:30:44Z day: '20' ddc: - '515' - '519' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe - _id: JaMa doi: 10.15479/at:ista:9733 ec_funded: 1 file: - access_level: open_access checksum: e88bb8ca43948abe060eb2d2fa719881 content_type: application/pdf creator: dfelicia date_created: 2021-08-19T14:03:48Z date_updated: 2021-09-06T09:28:56Z file_id: '9944' file_name: Thesis_FeliciangeliA.pdf file_size: 1958710 relation: main_file - access_level: closed checksum: 72810843abee83705853505b3f8348aa content_type: application/octet-stream creator: dfelicia date_created: 2021-08-19T14:06:35Z date_updated: 2022-03-10T12:13:57Z file_id: '9945' file_name: thesis.7z file_size: 3771669 relation: source_file file_date_updated: 2022-03-10T12:13:57Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '08' oa: 1 oa_version: Published Version page: '180' project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9787' relation: part_of_dissertation status: public - id: '9792' relation: part_of_dissertation status: public - id: '9225' relation: part_of_dissertation status: public - id: '9781' relation: part_of_dissertation status: public - id: '9791' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 title: The polaron at strong coupling tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '9791' 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.. article_number: '2107.03720 ' article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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. 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. . 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. short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.). date_created: 2021-08-06T08:49:45Z date_published: 2021-07-08T00:00:00Z date_updated: 2024-03-06T12:30:45Z day: '08' ddc: - '510' department: - _id: RoSe ec_funded: 1 external_id: arxiv: - '2107.03720' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2107.03720 month: '07' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 publication: arXiv publication_status: submitted related_material: record: - id: '10755' relation: later_version status: public - id: '9733' relation: dissertation_contains status: public status: public title: The effective mass problem for the Landau-Pekar equations type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '9781' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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. 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. 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. 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. short: D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622. date_created: 2021-08-06T07:34:16Z date_published: 2020-02-12T00:00:00Z date_updated: 2023-09-07T13:30:11Z day: '12' ddc: - '510' department: - _id: RoSe doi: 10.1137/19m126284x ec_funded: 1 external_id: arxiv: - '1904.08647 ' isi: - '000546967700022' has_accepted_license: '1' intvolume: ' 52' isi: 1 issue: '1' keyword: - Applied Mathematics - Computational Mathematics - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1904.08647 month: '02' oa: 1 oa_version: Preprint page: 605-622 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: SIAM Journal on Mathematical Analysis publication_identifier: eissn: - 1095-7154 issn: - 0036-1410 publication_status: published publisher: 'Society for Industrial & Applied Mathematics ' quality_controlled: '1' related_material: record: - id: '9733' relation: dissertation_contains status: public scopus_import: '1' status: public title: Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 52 year: '2020' ...