--- _id: '7900' abstract: - lang: eng text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation. article_number: '2060009' article_processing_charge: No article_type: original author: - first_name: Niels P full_name: Benedikter, Niels P id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87 last_name: Benedikter orcid: 0000-0002-1071-6091 citation: ama: Benedikter NP. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/s0129055x20600090 apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. World Scientific. https://doi.org/10.1142/s0129055x20600090 chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/s0129055x20600090. ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021. ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 33(1), 2060009. mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060009, World Scientific, 2021, doi:10.1142/s0129055x20600090. short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021). date_created: 2020-05-28T16:47:55Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-09-05T16:07:40Z day: '01' department: - _id: RoSe doi: 10.1142/s0129055x20600090 ec_funded: 1 external_id: arxiv: - '1910.08190' isi: - '000613313200010' intvolume: ' 33' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.08190 month: '01' 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: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific quality_controlled: '1' scopus_import: '1' status: public title: Bosonic collective excitations in Fermi gases type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 33 year: '2021' ... --- _id: '10852' abstract: - lang: eng text: ' We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.' acknowledgement: This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227). article_number: '2060012' article_processing_charge: No article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600120 apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120 chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120. ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021. ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012. mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120. short: R. Seiringer, Reviews in Mathematical Physics 33 (2021). date_created: 2022-03-18T08:11:34Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-05T16:08:02Z day: '01' department: - _id: RoSe doi: 10.1142/s0129055x20600120 ec_funded: 1 external_id: arxiv: - '1912.12509' isi: - '000613313200013' intvolume: ' 33' isi: 1 issue: '01' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.12509 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: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: The polaron at strong coupling type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 33 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: '10738' abstract: - lang: eng text: We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2. acknowledgement: "N. L. and R. S. gratefully acknowledge financial support by the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for stimulating discussions about the time-evolution of a polaron.\r\n" article_processing_charge: No article_type: original author: - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - 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: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 2021;14(7):2079-2100. doi:10.2140/APDE.2021.14.2079' apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/APDE.2021.14.2079' chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/APDE.2021.14.2079.' ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” Analysis and PDE, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.' ista: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021. The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.' mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:10.2140/APDE.2021.14.2079.' short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100. date_created: 2022-02-06T23:01:33Z date_published: 2021-11-10T00:00:00Z date_updated: 2023-10-17T11:26:45Z day: '10' department: - _id: RoSe doi: 10.2140/APDE.2021.14.2079 ec_funded: 1 external_id: arxiv: - '1904.12532' isi: - '000733976600004' intvolume: ' 14' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1904.12532 month: '11' oa: 1 oa_version: Preprint page: 2079-2100 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Analysis and PDE publication_identifier: eissn: - 1948-206X issn: - 2157-5045 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2021' ...