[{"related_material":{"record":[{"status":"public","id":"10850","relation":"part_of_dissertation"},{"id":"13207","relation":"part_of_dissertation","status":"public"}]},"type":"dissertation","ec_funded":1,"page":"206","day":"30","doi":"10.15479/at:ista:14374","publisher":"Institute of Science and Technology Austria","citation":{"chicago":"Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:14374\">https://doi.org/10.15479/at:ista:14374</a>.","ama":"Roos B. Boundary superconductivity in BCS theory. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:14374\">10.15479/at:ista:14374</a>","ieee":"B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023.","ista":"Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science and Technology Austria.","apa":"Roos, B. (2023). <i>Boundary superconductivity in BCS theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14374\">https://doi.org/10.15479/at:ista:14374</a>","mla":"Roos, Barbara. <i>Boundary Superconductivity in BCS Theory</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:14374\">10.15479/at:ista:14374</a>.","short":"B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"file_date_updated":"2023-10-06T11:38:01Z","date_created":"2023-09-28T14:23:04Z","supervisor":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"corr_author":"1","date_updated":"2026-04-07T13:27:39Z","OA_place":"publisher","has_accepted_license":"1","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"month":"09","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","title":"Boundary superconductivity in BCS theory","oa_version":"Published Version","year":"2023","_id":"14374","oa":1,"file":[{"file_size":2365702,"relation":"main_file","file_id":"14398","access_level":"open_access","creator":"broos","date_created":"2023-10-06T11:35:56Z","content_type":"application/pdf","date_updated":"2023-10-06T11:35:56Z","file_name":"phd-thesis-draft_pdfa_acrobat.pdf","checksum":"ef039ffc3de2cb8dee5b14110938e9b6"},{"date_updated":"2023-10-06T11:38:01Z","file_name":"Version5.zip","checksum":"81dcac33daeefaf0111db52f41bb1fd0","file_id":"14399","file_size":4691734,"relation":"source_file","content_type":"application/x-zip-compressed","access_level":"closed","date_created":"2023-10-06T11:38:01Z","creator":"broos"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","author":[{"orcid":"0000-0002-9071-5880","last_name":"Roos","full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"publication_status":"published","degree_awarded":"PhD","ddc":["515","539"],"status":"public","abstract":[{"text":"Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap  in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality.\r\n\r\nIn the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space.","lang":"eng"}],"date_published":"2023-09-30T00:00:00Z"},{"type":"journal_article","ec_funded":1,"related_material":{"record":[{"status":"public","id":"14374","relation":"dissertation_contains"}]},"publisher":"EMS Press","day":"18","doi":"10.4171/JST/439","page":"1507–1540","volume":12,"citation":{"chicago":"Hainzl, Christian, Barbara Roos, and Robert Seiringer. “Boundary Superconductivity in the BCS Model.” <i>Journal of Spectral Theory</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/JST/439\">https://doi.org/10.4171/JST/439</a>.","ama":"Hainzl C, Roos B, Seiringer R. Boundary superconductivity in the BCS model. <i>Journal of Spectral Theory</i>. 2023;12(4):1507–1540. doi:<a href=\"https://doi.org/10.4171/JST/439\">10.4171/JST/439</a>","ista":"Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 12(4), 1507–1540.","mla":"Hainzl, Christian, et al. “Boundary Superconductivity in the BCS Model.” <i>Journal of Spectral Theory</i>, vol. 12, no. 4, EMS Press, 2023, pp. 1507–1540, doi:<a href=\"https://doi.org/10.4171/JST/439\">10.4171/JST/439</a>.","apa":"Hainzl, C., Roos, B., &#38; Seiringer, R. (2023). Boundary superconductivity in the BCS model. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/439\">https://doi.org/10.4171/JST/439</a>","ieee":"C. Hainzl, B. Roos, and R. Seiringer, “Boundary superconductivity in the BCS model,” <i>Journal of Spectral Theory</i>, vol. 12, no. 4. EMS Press, pp. 1507–1540, 2023.","short":"C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540."},"publication":"Journal of Spectral Theory","corr_author":"1","external_id":{"isi":["000997933500008"],"arxiv":["2201.08090"]},"has_accepted_license":"1","date_updated":"2026-04-07T13:27:39Z","publication_identifier":{"issn":["1664-039X"],"eissn":["1664-0403"]},"quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        12","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)"},"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"date_created":"2023-07-10T16:35:45Z","file_date_updated":"2023-07-11T08:19:15Z","title":"Boundary superconductivity in the BCS model","oa_version":"Published Version","_id":"13207","issue":"4","year":"2023","month":"05","article_processing_charge":"No","ddc":["530"],"arxiv":1,"acknowledgement":"We thank Egor Babaev for encouraging us to study this problem, and Rupert Frank for many fruitful discussions. scussions. Funding. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 (Barbara Roos and Robert Seiringer) is gratefully acknowledged.","status":"public","abstract":[{"lang":"eng","text":"We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg–Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity."}],"date_published":"2023-05-18T00:00:00Z","scopus_import":"1","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"file":[{"content_type":"application/pdf","access_level":"open_access","creator":"alisjak","date_created":"2023-07-11T08:19:15Z","file_id":"13208","file_size":304619,"relation":"main_file","success":1,"checksum":"5501da33be010b5c81440438287584d5","date_updated":"2023-07-11T08:19:15Z","file_name":"2023_EMS_Hainzl.pdf"}],"license":"https://creativecommons.org/licenses/by/4.0/","author":[{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","orcid":"0000-0002-9071-5880","last_name":"Roos"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"publication_status":"published","article_type":"original","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}]},{"title":"Low-energy spectrum and dynamics of the weakly interacting Bose gas","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"oa_version":"Published Version","year":"2022","issue":"6","_id":"11783","month":"06","article_processing_charge":"Yes (via OA deal)","acknowledgement":"The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged.","arxiv":1,"ddc":["530"],"status":"public","scopus_import":"1","abstract":[{"lang":"eng","text":"We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix."}],"date_published":"2022-06-10T00:00:00Z","oa":1,"file":[{"file_name":"2022_JourMathPhysics_Bossmann.pdf","date_updated":"2022-08-11T07:03:02Z","checksum":"d0d32c338c1896680174be88c70968fa","success":1,"relation":"main_file","file_size":5957888,"file_id":"11784","date_created":"2022-08-11T07:03:02Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"author":[{"first_name":"Lea","full_name":"Bossmann, Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann","orcid":"0000-0002-6854-1343"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"publication_status":"published","article_type":"original","ec_funded":1,"type":"journal_article","publisher":"AIP Publishing","day":"10","doi":"10.1063/5.0089983","volume":63,"citation":{"chicago":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0089983\">https://doi.org/10.1063/5.0089983</a>.","ama":"Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. 2022;63(6). doi:<a href=\"https://doi.org/10.1063/5.0089983\">10.1063/5.0089983</a>","ieee":"L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6. AIP Publishing, 2022.","ista":"Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102.","mla":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0089983\">10.1063/5.0089983</a>.","apa":"Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0089983\">https://doi.org/10.1063/5.0089983</a>","short":"L. Bossmann, Journal of Mathematical Physics 63 (2022)."},"publication":"Journal of Mathematical Physics","external_id":{"isi":["000809648100002"],"arxiv":["2203.00730"]},"corr_author":"1","date_updated":"2025-04-14T07:43:58Z","has_accepted_license":"1","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"intvolume":"        63","language":[{"iso":"eng"}],"quality_controlled":"1","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_number":"061102","department":[{"_id":"RoSe"}],"date_created":"2022-08-11T06:37:52Z","file_date_updated":"2022-08-11T07:03:02Z"},{"article_number":"9","department":[{"_id":"RoSe"}],"date_created":"2022-08-18T07:23:26Z","file_date_updated":"2022-08-18T08:09:00Z","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)"},"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"intvolume":"       188","language":[{"iso":"eng"}],"quality_controlled":"1","external_id":{"isi":["000805175000001"]},"corr_author":"1","date_updated":"2025-04-14T07:26:59Z","has_accepted_license":"1","publication":"Journal of Statistical Physics","volume":188,"citation":{"chicago":"Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02940-4\">https://doi.org/10.1007/s10955-022-02940-4</a>.","ama":"Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting bosons. <i>Journal of Statistical Physics</i>. 2022;188. doi:<a href=\"https://doi.org/10.1007/s10955-022-02940-4\">10.1007/s10955-022-02940-4</a>","ieee":"S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly interacting bosons,” <i>Journal of Statistical Physics</i>, vol. 188. Springer Nature, 2022.","ista":"Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9.","apa":"Rademacher, S. A. E., &#38; Seiringer, R. (2022). Large deviation estimates for weakly interacting bosons. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02940-4\">https://doi.org/10.1007/s10955-022-02940-4</a>","mla":"Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” <i>Journal of Statistical Physics</i>, vol. 188, 9, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02940-4\">10.1007/s10955-022-02940-4</a>.","short":"S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022)."},"type":"journal_article","ec_funded":1,"day":"01","doi":"10.1007/s10955-022-02940-4","publisher":"Springer Nature","author":[{"last_name":"Rademacher","orcid":"0000-0001-5059-4466","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_type":"original","publication_status":"published","oa":1,"file":[{"success":1,"checksum":"44418cb44f07fa21ed3907f85abf7f39","file_name":"2022_JournalStatisticalPhysics_Rademacher.pdf","date_updated":"2022-08-18T08:09:00Z","content_type":"application/pdf","creator":"dernst","date_created":"2022-08-18T08:09:00Z","access_level":"open_access","file_id":"11922","file_size":483481,"relation":"main_file"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"status":"public","date_published":"2022-07-01T00:00:00Z","abstract":[{"lang":"eng","text":"We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order."}],"scopus_import":"1","acknowledgement":"The authors thank Gérard Ben Arous for pointing out the question of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding provided by IST Austria.","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","month":"07","oa_version":"Published Version","year":"2022","_id":"11917","title":"Large deviation estimates for weakly interacting bosons","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"]},{"publication_identifier":{"issn":["0022-2488"]},"quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        63","corr_author":"1","external_id":{"arxiv":["2112.04817"],"isi":["000844402500001"]},"has_accepted_license":"1","date_updated":"2025-04-14T07:26:59Z","department":[{"_id":"RoSe"}],"article_number":"081902","date_created":"2022-09-11T22:01:56Z","file_date_updated":"2022-09-12T07:35:34Z","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)"},"volume":63,"citation":{"chicago":"Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0086712\">https://doi.org/10.1063/5.0086712</a>.","ama":"Rademacher SAE. Dependent random variables in quantum dynamics. <i>Journal of Mathematical Physics</i>. 2022;63(8). doi:<a href=\"https://doi.org/10.1063/5.0086712\">10.1063/5.0086712</a>","mla":"Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 8, 081902, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0086712\">10.1063/5.0086712</a>.","ista":"Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 63(8), 081902.","apa":"Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0086712\">https://doi.org/10.1063/5.0086712</a>","ieee":"S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 8. AIP Publishing, 2022.","short":"S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022)."},"ec_funded":1,"type":"journal_article","publisher":"AIP Publishing","doi":"10.1063/5.0086712","day":"25","publication":"Journal of Mathematical Physics","status":"public","abstract":[{"text":"We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem.","lang":"eng"}],"scopus_import":"1","date_published":"2022-08-25T00:00:00Z","ddc":["510"],"arxiv":1,"acknowledgement":"S.R. would like to thank Robert Seiringer and Benedikt Stufler for helpful discussions. Funding from the European Union’s Horizon 2020 Research and Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged.","author":[{"last_name":"Rademacher","orcid":"0000-0001-5059-4466","id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira"}],"publication_status":"published","article_type":"original","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"file":[{"file_name":"2022_JourMathPhysics_Rademacher.pdf","date_updated":"2022-09-12T07:35:34Z","success":1,"checksum":"e6fb0cf3f0327739c5e69a2cfc4020eb","file_id":"12089","file_size":4552261,"relation":"main_file","content_type":"application/pdf","date_created":"2022-09-12T07:35:34Z","creator":"dernst","access_level":"open_access"}],"oa_version":"Published Version","_id":"12083","issue":"8","year":"2022","title":"Dependent random variables in quantum dynamics","article_processing_charge":"No","month":"08"},{"project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"article_type":"original","publication_status":"published","author":[{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"last_name":"Lieb","full_name":"Lieb, Elliott H.","first_name":"Elliott H."},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","isi":1,"oa":1,"scopus_import":"1","abstract":[{"text":"The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.","lang":"eng"}],"date_published":"2022-09-15T00:00:00Z","status":"public","acknowledgement":"We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done.","arxiv":1,"article_processing_charge":"No","month":"09","year":"2022","issue":"5","_id":"12246","oa_version":"Preprint","title":"Improved Lieb–Oxford bound on the indirect and exchange energies","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2023-01-16T09:53:54Z","article_number":"92","department":[{"_id":"RoSe"}],"intvolume":"       112","language":[{"iso":"eng"}],"quality_controlled":"1","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"date_updated":"2025-04-14T07:26:59Z","external_id":{"arxiv":["2203.12473"],"isi":["000854762600001"]},"publication":"Letters in Mathematical Physics","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.12473","open_access":"1"}],"citation":{"ama":"Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. <i>Letters in Mathematical Physics</i>. 2022;112(5). doi:<a href=\"https://doi.org/10.1007/s11005-022-01584-5\">10.1007/s11005-022-01584-5</a>","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11005-022-01584-5\">https://doi.org/10.1007/s11005-022-01584-5</a>.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” <i>Letters in Mathematical Physics</i>, vol. 112, no. 5. Springer Nature, 2022.","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-022-01584-5\">https://doi.org/10.1007/s11005-022-01584-5</a>","ista":"Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92.","mla":"Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 5, 92, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11005-022-01584-5\">10.1007/s11005-022-01584-5</a>."},"volume":112,"publisher":"Springer Nature","day":"15","doi":"10.1007/s11005-022-01584-5","ec_funded":1,"type":"journal_article"},{"author":[{"last_name":"Ljubotina","orcid":"0000-0003-0038-7068","full_name":"Ljubotina, Marko","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","first_name":"Marko"},{"first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880"},{"last_name":"Abanin","first_name":"Dmitry A.","full_name":"Abanin, Dmitry A."},{"orcid":"0000-0002-2399-5827","last_name":"Serbyn","first_name":"Maksym","full_name":"Serbyn, Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020"}],"article_type":"original","publication_status":"published","oa":1,"file":[{"file_name":"2022_PRXQuantum_Ljubotina.pdf","date_updated":"2023-01-30T11:02:50Z","checksum":"ef8f0a1b5a019b3958009162de0fa4c3","success":1,"file_size":7661905,"relation":"main_file","file_id":"12457","creator":"dernst","date_created":"2023-01-30T11:02:50Z","access_level":"open_access","content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","abstract":[{"text":"Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.","lang":"eng"}],"date_published":"2022-09-23T00:00:00Z","scopus_import":"1","acknowledgement":"We thank A. A. Michailidis for insightful discussions. M.L. and M.S. acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 850899). D.A. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 864597) and by the Swiss National Science Foundation. The infinite TEBD simulations were performed using the ITensor library [67].","ddc":["530"],"arxiv":1,"article_processing_charge":"No","month":"09","oa_version":"Published Version","year":"2022","issue":"3","_id":"12276","title":"Optimal steering of matrix product states and quantum many-body scars","keyword":["General Medicine"],"article_number":"030343","department":[{"_id":"MaSe"},{"_id":"RoSe"}],"date_created":"2023-01-16T10:01:56Z","file_date_updated":"2023-01-30T11:02:50Z","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)"},"publication_identifier":{"eissn":["2691-3399"]},"intvolume":"         3","language":[{"iso":"eng"}],"quality_controlled":"1","external_id":{"arxiv":["2204.02899"]},"corr_author":"1","date_updated":"2025-04-14T07:52:07Z","has_accepted_license":"1","publication":"PRX Quantum","volume":3,"citation":{"ieee":"M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, “Optimal steering of matrix product states and quantum many-body scars,” <i>PRX Quantum</i>, vol. 3, no. 3. American Physical Society, 2022.","apa":"Ljubotina, M., Roos, B., Abanin, D. A., &#38; Serbyn, M. (2022). Optimal steering of matrix product states and quantum many-body scars. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/prxquantum.3.030343\">https://doi.org/10.1103/prxquantum.3.030343</a>","mla":"Ljubotina, Marko, et al. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” <i>PRX Quantum</i>, vol. 3, no. 3, 030343, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/prxquantum.3.030343\">10.1103/prxquantum.3.030343</a>.","ista":"Ljubotina M, Roos B, Abanin DA, Serbyn M. 2022. Optimal steering of matrix product states and quantum many-body scars. PRX Quantum. 3(3), 030343.","short":"M. Ljubotina, B. Roos, D.A. Abanin, M. Serbyn, PRX Quantum 3 (2022).","chicago":"Ljubotina, Marko, Barbara Roos, Dmitry A. Abanin, and Maksym Serbyn. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” <i>PRX Quantum</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/prxquantum.3.030343\">https://doi.org/10.1103/prxquantum.3.030343</a>.","ama":"Ljubotina M, Roos B, Abanin DA, Serbyn M. Optimal steering of matrix product states and quantum many-body scars. <i>PRX Quantum</i>. 2022;3(3). doi:<a href=\"https://doi.org/10.1103/prxquantum.3.030343\">10.1103/prxquantum.3.030343</a>"},"ec_funded":1,"type":"journal_article","doi":"10.1103/prxquantum.3.030343","publisher":"American Physical Society","day":"23"},{"article_processing_charge":"Yes (via OA deal)","month":"01","year":"2022","issue":"1","_id":"10755","oa_version":"Published Version","title":"The effective mass problem for the Landau-Pekar equations","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_type":"original","publication_status":"published","author":[{"first_name":"Dario","full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530"},{"last_name":"Rademacher","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"file":[{"file_id":"10757","relation":"main_file","file_size":1132380,"content_type":"application/pdf","date_created":"2022-02-14T08:20:19Z","creator":"dernst","access_level":"open_access","file_name":"2022_JournalPhysicsA_Feliciangeli.pdf","date_updated":"2022-02-14T08:20:19Z","success":1,"checksum":"0875e562705563053d6dd98fba4d8578"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"scopus_import":"1","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"}],"date_published":"2022-01-19T00:00:00Z","status":"public","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.","arxiv":1,"ddc":["510"],"publication":"Journal of Physics A: Mathematical and Theoretical","citation":{"chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing, 2022. <a href=\"https://doi.org/10.1088/1751-8121/ac3947\">https://doi.org/10.1088/1751-8121/ac3947</a>.","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(1). doi:<a href=\"https://doi.org/10.1088/1751-8121/ac3947\">10.1088/1751-8121/ac3947</a>","apa":"Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2022). The effective mass problem for the Landau-Pekar equations. <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1751-8121/ac3947\">https://doi.org/10.1088/1751-8121/ac3947</a>","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 1, 015201, IOP Publishing, 2022, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac3947\">10.1088/1751-8121/ac3947</a>.","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.","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” <i>Journal of Physics A: Mathematical and Theoretical</i>, 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)."},"volume":55,"day":"19","publisher":"IOP Publishing","doi":"10.1088/1751-8121/ac3947","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9791"}]},"ec_funded":1,"type":"journal_article","date_created":"2022-02-13T23:01:35Z","file_date_updated":"2022-02-14T08:20:19Z","article_number":"015201","department":[{"_id":"RoSe"}],"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)"},"intvolume":"        55","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"date_updated":"2025-04-15T06:54:54Z","has_accepted_license":"1","external_id":{"arxiv":["2107.03720"]},"corr_author":"1"},{"arxiv":1,"acknowledgement":"NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM). RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates,” and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through the ERC-AdG CLaQS (Grant Agreement No. 834782).","status":"public","scopus_import":"1","abstract":[{"lang":"eng","text":"We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle–hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many-body evolution can be approximated in Fock space norm by a quasi-free bosonic evolution of the collective particle–hole excitations."}],"date_published":"2022-05-01T00:00:00Z","oa":1,"isi":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-1071-6091","last_name":"Benedikter","first_name":"Niels P","full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Nam","full_name":"Nam, Phan Thành","first_name":"Phan Thành"},{"last_name":"Porta","full_name":"Porta, Marcello","first_name":"Marcello"},{"last_name":"Schlein","full_name":"Schlein, Benjamin","first_name":"Benjamin"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert"}],"article_type":"original","publication_status":"published","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"title":"Bosonization of fermionic many-body dynamics","oa_version":"Preprint","issue":"5","_id":"10537","year":"2022","month":"05","article_processing_charge":"No","external_id":{"arxiv":["2103.08224"],"isi":["000725405700001"]},"date_updated":"2025-04-14T07:26:53Z","publication_identifier":{"issn":["1424-0637"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        23","department":[{"_id":"RoSe"}],"date_created":"2021-12-12T23:01:28Z","ec_funded":1,"type":"journal_article","day":"01","doi":"10.1007/s00023-021-01136-y","publisher":"Springer Nature","page":"1725-1764","volume":23,"citation":{"chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-021-01136-y\">https://doi.org/10.1007/s00023-021-01136-y</a>.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic many-body dynamics. <i>Annales Henri Poincaré</i>. 2022;23(5):1725-1764. doi:<a href=\"https://doi.org/10.1007/s00023-021-01136-y\">10.1007/s00023-021-01136-y</a>","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2022). Bosonization of fermionic many-body dynamics. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01136-y\">https://doi.org/10.1007/s00023-021-01136-y</a>","mla":"Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.” <i>Annales Henri Poincaré</i>, vol. 23, no. 5, Springer Nature, 2022, pp. 1725–64, doi:<a href=\"https://doi.org/10.1007/s00023-021-01136-y\">10.1007/s00023-021-01136-y</a>.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2022. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. 23(5), 1725–1764.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization of fermionic many-body dynamics,” <i>Annales Henri Poincaré</i>, vol. 23, no. 5. Springer Nature, pp. 1725–1764, 2022.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri Poincaré 23 (2022) 1725–1764."},"main_file_link":[{"url":"https://arxiv.org/abs/2103.08224","open_access":"1"}],"publication":"Annales Henri Poincaré"},{"corr_author":"1","external_id":{"isi":["000833007200002"]},"has_accepted_license":"1","date_updated":"2026-04-07T13:01:40Z","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"       189","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)"},"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"article_number":"5","file_date_updated":"2022-08-08T07:36:34Z","date_created":"2022-08-05T11:36:56Z","type":"journal_article","ec_funded":1,"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"},{"status":"public","id":"18135","relation":"dissertation_contains"}]},"doi":"10.1007/s10955-022-02965-9","publisher":"Springer Nature","day":"29","volume":189,"citation":{"short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” <i>Journal of Statistical Physics</i>, vol. 189. Springer Nature, 2022.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2022). The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>, vol. 189, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. 2022;189. doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>."},"publication":"Journal of Statistical Physics","ddc":["530"],"acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","status":"public","scopus_import":"1","abstract":[{"text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.","lang":"eng"}],"date_published":"2022-07-29T00:00:00Z","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","isi":1,"file":[{"date_created":"2022-08-08T07:36:34Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":419563,"file_id":"11746","checksum":"b398c4dbf65f71d417981d6e366427e9","success":1,"file_name":"2022_JourStatisticalPhysics_Henheik.pdf","date_updated":"2022-08-08T07:36:34Z"}],"author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Lauritsen","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"article_type":"original","publication_status":"published","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"title":"The BCS energy gap at high density","oa_version":"Published Version","_id":"11732","year":"2022","month":"07","article_processing_charge":"Yes (via OA deal)"},{"abstract":[{"text":"We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1.","lang":"eng"}],"date_published":"2022-06-15T00:00:00Z","scopus_import":"1","status":"public","arxiv":1,"ddc":["510"],"acknowledgement":"We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.","publication_status":"published","article_type":"original","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","first_name":"Barbara","orcid":"0000-0002-9071-5880","last_name":"Roos"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"63efcefaa1f2717244ef5407bd564426","success":1,"date_updated":"2022-08-02T10:37:55Z","file_name":"2022_JourFunctionalAnalysis_Roos.pdf","access_level":"open_access","creator":"dernst","date_created":"2022-08-02T10:37:55Z","content_type":"application/pdf","file_size":631391,"relation":"main_file","file_id":"11720"}],"oa":1,"issue":"12","_id":"10850","year":"2022","oa_version":"Published Version","keyword":["Analysis"],"title":"Two-particle bound states at interfaces and corners","article_processing_charge":"Yes (via OA deal)","month":"06","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"       282","publication_identifier":{"issn":["0022-1236"]},"has_accepted_license":"1","date_updated":"2026-04-07T13:27:39Z","corr_author":"1","external_id":{"arxiv":["2105.04874"],"isi":["000795160200009"]},"date_created":"2022-03-16T08:41:53Z","file_date_updated":"2022-08-02T10:37:55Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"article_number":"109455","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)"},"citation":{"chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>.","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. 2022;282(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>","apa":"Roos, B., &#38; Seiringer, R. (2022). Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>","ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.","mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>, vol. 282, no. 12, 109455, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>.","ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” <i>Journal of Functional Analysis</i>, vol. 282, no. 12. Elsevier, 2022.","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022)."},"volume":282,"doi":"10.1016/j.jfa.2022.109455","day":"15","publisher":"Elsevier","type":"journal_article","ec_funded":1,"related_material":{"record":[{"status":"public","id":"14374","relation":"dissertation_contains"}]},"publication":"Journal of Functional Analysis"},{"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file":[{"date_updated":"2022-07-05T08:12:56Z","file_name":"thes1_no_isbn_2_1b.pdf","success":1,"checksum":"7970714a20a6052f75fb27a6c3e9976e","file_id":"11486","relation":"main_file","file_size":1830973,"content_type":"application/pdf","access_level":"open_access","creator":"kmysliwy","date_created":"2022-07-05T08:12:56Z"},{"file_name":"thes_source.zip","date_updated":"2022-07-05T08:17:12Z","checksum":"647a2011fdf56277096c9350fefe1097","relation":"source_file","file_size":5831060,"file_id":"11487","creator":"kmysliwy","date_created":"2022-07-05T08:15:52Z","access_level":"closed","content_type":"application/zip"}],"oa":1,"publication_status":"published","project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Mysliwy","first_name":"Krzysztof","full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87"}],"ddc":["515","539"],"degree_awarded":"PhD","date_published":"2022-07-01T00:00:00Z","abstract":[{"text":"The polaron model is a basic model of quantum field theory describing a single particle\r\ninteracting with a bosonic field. It arises in many physical contexts. We are mostly concerned\r\nwith models applicable in the context of an impurity atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving in polar crystals.\r\nThe model has a simple structure in which the interaction of the particle with the field is given\r\nby a term linear in the field’s creation and annihilation operators. In this work, we investigate\r\nthe properties of this model by providing rigorous estimates on various energies relevant to the\r\nproblem. The estimates are obtained, for the most part, by suitable operator techniques which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe first application of these techniques is to derive the polaron model rigorously from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective theory for this problem.\r\nIn the second part, we investigate rigorously the ground state of the model at fixed momentum\r\nand for large values of the coupling constant. Qualitatively, the system is expected to display\r\na transition from the quasi-particle behavior at small momenta, where the dispersion relation\r\nis parabolic and the particle moves through the medium dragging along a cloud of phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates and emits free phonons.\r\nAt the same time, in the strong coupling regime, the bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst studied by Landau and Pekar in the 1940s. For polaron models with regularized form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove\r\nthat for a large window of momenta below the radiation threshold, the energy-momentum\r\nrelation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is\r\nof the optical type and the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe regular case, this requires the inclusion of the quantum fluctuations of the phonon field,\r\nwhich makes the problem considerably more difficult.\r\nThe results are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na proof of the divergence of the effective mass with the coupling constant for a wide class of\r\npolaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model\r\nand the application of the techniques used for its removal for the energy estimates.\r\n","lang":"eng"}],"status":"public","month":"07","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"title":"Polarons in Bose gases and polar crystals: Some rigorous energy estimates","_id":"11473","year":"2022","oa_version":"Published Version","acknowledged_ssus":[{"_id":"SSU"}],"date_created":"2022-06-30T12:15:03Z","file_date_updated":"2022-07-05T08:17:12Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"OA_place":"publisher","has_accepted_license":"1","date_updated":"2026-04-07T14:14:52Z","corr_author":"1","supervisor":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"doi":"10.15479/at:ista:11473","day":"01","publisher":"Institute of Science and Technology Austria","page":"138","ec_funded":1,"type":"dissertation","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10564"},{"status":"public","relation":"part_of_dissertation","id":"8705"}]},"citation":{"ieee":"K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy estimates,” Institute of Science and Technology Austria, 2022.","ista":"Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria.","mla":"Mysliwy, Krzysztof. <i>Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates</i>. Institute of Science and Technology Austria, 2022, doi:<a href=\"https://doi.org/10.15479/at:ista:11473\">10.15479/at:ista:11473</a>.","apa":"Mysliwy, K. (2022). <i>Polarons in Bose gases and polar crystals: Some rigorous energy estimates</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:11473\">https://doi.org/10.15479/at:ista:11473</a>","short":"K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates, Institute of Science and Technology Austria, 2022.","chicago":"Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates.” Institute of Science and Technology Austria, 2022. <a href=\"https://doi.org/10.15479/at:ista:11473\">https://doi.org/10.15479/at:ista:11473</a>.","ama":"Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. 2022. doi:<a href=\"https://doi.org/10.15479/at:ista:11473\">10.15479/at:ista:11473</a>"}},{"publisher":"Springer Nature","day":"01","doi":"10.1007/s10955-021-02851-w","type":"journal_article","ec_funded":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"11473"}]},"citation":{"chicago":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-021-02851-w\">https://doi.org/10.1007/s10955-021-02851-w</a>.","ama":"Mysliwy K, Seiringer R. Polaron models with regular interactions at strong coupling. <i>Journal of Statistical Physics</i>. 2022;186(1). doi:<a href=\"https://doi.org/10.1007/s10955-021-02851-w\">10.1007/s10955-021-02851-w</a>","apa":"Mysliwy, K., &#38; Seiringer, R. (2022). Polaron models with regular interactions at strong coupling. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-021-02851-w\">https://doi.org/10.1007/s10955-021-02851-w</a>","mla":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” <i>Journal of Statistical Physics</i>, vol. 186, no. 1, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-021-02851-w\">10.1007/s10955-021-02851-w</a>.","ista":"Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5.","ieee":"K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at strong coupling,” <i>Journal of Statistical Physics</i>, vol. 186, no. 1. Springer Nature, 2022.","short":"K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022)."},"volume":186,"publication":"Journal of Statistical Physics","has_accepted_license":"1","date_updated":"2026-04-07T14:14:51Z","corr_author":"1","external_id":{"isi":["000726275600001"],"arxiv":["2106.09328"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"       186","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"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)"},"file_date_updated":"2022-02-02T14:24:41Z","date_created":"2021-12-19T23:01:32Z","department":[{"_id":"RoSe"}],"article_number":"5","title":"Polaron models with regular interactions at strong coupling","issue":"1","_id":"10564","year":"2022","oa_version":"Published Version","month":"01","article_processing_charge":"Yes (via OA deal)","ddc":["530"],"arxiv":1,"acknowledgement":"Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant Agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.) is gratefully acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","date_published":"2022-01-01T00:00:00Z","scopus_import":"1","abstract":[{"text":"We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.","lang":"eng"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"file":[{"success":1,"checksum":"da03f6d293c4b9802091bce9471b1d29","date_updated":"2022-02-02T14:24:41Z","file_name":"2022_JournalStatPhys_Myśliwy.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2022-02-02T14:24:41Z","creator":"cchlebak","file_id":"10716","relation":"main_file","file_size":434957}],"oa":1,"publication_status":"published","article_type":"original","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"author":[{"full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","last_name":"Mysliwy"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}]},{"ddc":["500"],"degree_awarded":"PhD","abstract":[{"text":"The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that\r\nis broken on the level of the corresponding effective theory. In particular we are going to\r\ninvestigate translation-invariant Bose gases in the mean field limit, effectively described by\r\nthe Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed by the Pekar functional. The latter is a model describing the interaction between a\r\ncharged particle and the optical modes of a polar crystal. Regarding the former, we assume in\r\naddition that the particles in the gas are unconfined, and typically we will consider particles\r\nthat are subject to an attractive interaction. In both cases the ground state energy of the\r\nHamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe contrary there exists a whole invariant orbit of minimizers for the corresponding effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken symmetry of the effective\r\ntheory, make the study significantly more involved and it is the content of this thesis to\r\ndevelop a frameworks which allows for a systematic way to circumvent these issues.\r\nIt is a well-established result that the ground state energy of Bose gases in the mean field limit,\r\nas well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is\r\nto leading order given by the minimal energy of the corresponding effective theory. As part\r\nof this thesis we identify the sub-leading term in the expansion of the ground state energy,\r\nwhich can be interpreted as the quantum correction to the classical energy, since the effective\r\ntheories under consideration can be seen as classical counterparts.\r\nWe are further going to establish an asymptotic expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic expression agrees with the energy-momentum relation of a free particle having\r\nan effectively increased mass, and we find that this effectively increased mass agrees with the\r\nconjectured value in the physics literature.\r\nIn addition we will discuss two unrelated papers written by the author during his stay at ISTA\r\nin the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe second one provides a classification of those vector fields defined on a given manifold\r\nthat can be written as the gradient of a given functional with respect to a suitable metric,\r\nprovided that some mild smoothness assumptions hold. This classification is subsequently\r\nused to identify those quantum Markov semigroups that can be written as a gradient flow of\r\nthe relative entropy.\r\n","lang":"eng"}],"date_published":"2022-12-15T00:00:00Z","status":"public","file":[{"relation":"main_file","file_size":3095225,"file_id":"12391","date_created":"2023-01-26T10:02:34Z","creator":"cchlebak","access_level":"open_access","content_type":"application/pdf","file_name":"Brooks_Thesis.pdf","date_updated":"2023-01-26T10:02:34Z","checksum":"b31460e937f33b557abb40ebef02b567","success":1},{"file_id":"12392","relation":"source_file","file_size":809842,"content_type":"application/octet-stream","access_level":"closed","creator":"cchlebak","date_created":"2023-01-26T10:02:42Z","date_updated":"2023-01-26T10:02:42Z","file_name":"Brooks_Thesis.tex","checksum":"9751869fa5e7981588ad4228f4fd4bd6"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"publication_status":"published","author":[{"first_name":"Morris","full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928"}],"title":"Translation-invariant quantum systems with effectively broken symmetry","year":"2022","_id":"12390","oa_version":"Published Version","month":"12","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"date_updated":"2026-04-16T08:20:52Z","OA_place":"publisher","has_accepted_license":"1","supervisor":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"corr_author":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"file_date_updated":"2023-01-26T10:02:42Z","date_created":"2023-01-26T10:00:42Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"page":"196","day":"15","doi":"10.15479/at:ista:12390","publisher":"Institute of Science and Technology Austria","related_material":{"record":[{"status":"public","id":"9005","relation":"part_of_dissertation"}]},"ec_funded":1,"type":"dissertation","citation":{"short":"M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022.","ieee":"M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022.","mla":"Brooks, Morris. <i>Translation-Invariant Quantum Systems with Effectively Broken Symmetry</i>. Institute of Science and Technology Austria, 2022, doi:<a href=\"https://doi.org/10.15479/at:ista:12390\">10.15479/at:ista:12390</a>.","apa":"Brooks, M. (2022). <i>Translation-invariant quantum systems with effectively broken symmetry</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:12390\">https://doi.org/10.15479/at:ista:12390</a>","ista":"Brooks M. 2022. Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria.","ama":"Brooks M. Translation-invariant quantum systems with effectively broken symmetry. 2022. doi:<a href=\"https://doi.org/10.15479/at:ista:12390\">10.15479/at:ista:12390</a>","chicago":"Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively Broken Symmetry.” Institute of Science and Technology Austria, 2022. <a href=\"https://doi.org/10.15479/at:ista:12390\">https://doi.org/10.15479/at:ista:12390</a>."}},{"citation":{"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.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>.","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. <i>Pure and Applied Analysis</i>. 2021;3(4):653-676. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>","apa":"Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>","mla":"Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>.","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.","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,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021.","short":"N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676."},"volume":3,"doi":"10.2140/paa.2021.3.653","publisher":"Mathematical Sciences Publishers","day":"01","page":"653-676","ec_funded":1,"type":"journal_article","publication":"Pure and Applied Analysis","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2005.02098"}],"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"         3","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"date_updated":"2025-04-14T07:27:00Z","corr_author":"1","external_id":{"arxiv":["2005.02098"]},"date_created":"2024-01-28T23:01:43Z","department":[{"_id":"RoSe"}],"issue":"4","_id":"14889","year":"2021","oa_version":"Preprint","title":"Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron","article_processing_charge":"No","month":"10","scopus_import":"1","abstract":[{"lang":"eng","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."}],"date_published":"2021-10-01T00:00:00Z","status":"public","arxiv":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.","publication_status":"published","article_type":"original","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"orcid":"0000-0002-0495-6822","last_name":"Leopold","first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","last_name":"Mitrouskas"},{"first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466","last_name":"Rademacher"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1},{"month":"10","article_processing_charge":"No","title":"Beyond Bogoliubov dynamics","year":"2021","_id":"14890","issue":"4","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"publication_status":"published","article_type":"original","author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea","first_name":"Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann"},{"first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat"},{"first_name":"Peter","full_name":"Pickl, Peter","last_name":"Pickl"},{"full_name":"Soffer, Avy","first_name":"Avy","last_name":"Soffer"}],"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.","arxiv":1,"scopus_import":"1","date_published":"2021-10-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.11004","open_access":"1"}],"publication":"Pure and Applied Analysis","page":"677-726","doi":"10.2140/paa.2021.3.677","day":"01","publisher":"Mathematical Sciences Publishers","ec_funded":1,"type":"journal_article","citation":{"ama":"Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. 2021;3(4):677-726. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>","chicago":"Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>.","short":"L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726.","apa":"Bossmann, L., Petrat, S. P., Pickl, P., &#38; Soffer, A. (2021). Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>","ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726.","mla":"Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>.","ieee":"L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021."},"volume":3,"date_created":"2024-01-28T23:01:43Z","department":[{"_id":"RoSe"}],"date_updated":"2025-04-14T07:44:02Z","external_id":{"arxiv":["1912.11004"]},"corr_author":"1","intvolume":"         3","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]}},{"oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"checksum":"d0e44b95f36c9e06724f66832af0f8c3","date_updated":"2022-01-03T10:15:05Z","file_name":"2021_Atoms_Brooks.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2022-01-03T10:15:05Z","creator":"alisjak","file_id":"10592","relation":"main_file","file_size":303070}],"author":[{"first_name":"Morris","full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","orcid":"0000-0002-6249-0928","last_name":"Brooks"},{"orcid":"0000-0002-6990-7802","last_name":"Lemeshko","first_name":"Mikhail","full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Lundholm, Douglas","first_name":"Douglas","last_name":"Lundholm"},{"orcid":"0000-0001-5973-0874","last_name":"Yakaboylu","full_name":"Yakaboylu, Enderalp","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","first_name":"Enderalp"}],"article_type":"original","publication_status":"published","ddc":["530"],"arxiv":1,"acknowledgement":"D. Lundholm acknowledges financial support from the Göran Gustafsson Foundation (grant no. 1804).","status":"public","date_published":"2021-12-02T00:00:00Z","scopus_import":"1","abstract":[{"text":"Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle","lang":"eng"}],"month":"12","article_processing_charge":"Yes","keyword":["anyons","quasiparticles","Quantum Hall Effect","topological states of matter"],"title":"Emergence of anyons on the two-sphere in molecular impurities","oa_version":"Published Version","issue":"4","_id":"10585","year":"2021","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)"},"department":[{"_id":"MiLe"},{"_id":"RoSe"}],"article_number":"106","file_date_updated":"2022-01-03T10:15:05Z","date_created":"2022-01-02T23:01:33Z","corr_author":"1","external_id":{"arxiv":["2108.06966"]},"has_accepted_license":"1","date_updated":"2024-10-09T21:01:20Z","publication_identifier":{"eissn":["2218-2004"]},"quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"         9","publication":"Atoms","type":"journal_article","day":"02","doi":"10.3390/atoms9040106","publisher":"MDPI","volume":9,"citation":{"chicago":"Brooks, Morris, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” <i>Atoms</i>. MDPI, 2021. <a href=\"https://doi.org/10.3390/atoms9040106\">https://doi.org/10.3390/atoms9040106</a>.","ama":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Emergence of anyons on the two-sphere in molecular impurities. <i>Atoms</i>. 2021;9(4). doi:<a href=\"https://doi.org/10.3390/atoms9040106\">10.3390/atoms9040106</a>","ista":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 9(4), 106.","mla":"Brooks, Morris, et al. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” <i>Atoms</i>, vol. 9, no. 4, 106, MDPI, 2021, doi:<a href=\"https://doi.org/10.3390/atoms9040106\">10.3390/atoms9040106</a>.","apa":"Brooks, M., Lemeshko, M., Lundholm, D., &#38; Yakaboylu, E. (2021). Emergence of anyons on the two-sphere in molecular impurities. <i>Atoms</i>. MDPI. <a href=\"https://doi.org/10.3390/atoms9040106\">https://doi.org/10.3390/atoms9040106</a>","ieee":"M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Emergence of anyons on the two-sphere in molecular impurities,” <i>Atoms</i>, vol. 9, no. 4. MDPI, 2021.","short":"M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Atoms 9 (2021)."}},{"publication":"Analysis and PDE","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.12532"}],"citation":{"ieee":"N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” <i>Analysis and PDE</i>, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.","mla":"Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>.","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.","apa":"Leopold, N. K., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021).  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>","short":"N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100.","chicago":"Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>.","ama":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R.  The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. 2021;14(7):2079-2100. doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>"},"volume":14,"day":"10","publisher":"Mathematical Sciences Publishers","doi":"10.2140/APDE.2021.14.2079","page":"2079-2100","ec_funded":1,"type":"journal_article","date_created":"2022-02-06T23:01:33Z","department":[{"_id":"RoSe"}],"quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        14","publication_identifier":{"eissn":["1948-206X"],"issn":["2157-5045"]},"date_updated":"2025-04-14T07:26:53Z","corr_author":"1","external_id":{"arxiv":["1904.12532"],"isi":["000733976600004"]},"article_processing_charge":"No","month":"11","issue":"7","_id":"10738","year":"2021","oa_version":"Preprint","title":" The Landau–Pekar equations: Adiabatic theorem and accuracy","publication_status":"published","article_type":"original","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"author":[{"first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","last_name":"Leopold"},{"first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466","last_name":"Rademacher"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2021-11-10T00:00:00Z","scopus_import":"1","abstract":[{"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.","lang":"eng"}],"status":"public","arxiv":1,"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"},{"main_file_link":[{"url":"https://arxiv.org/abs/1912.12509","open_access":"1"}],"publication":"Reviews in Mathematical Physics","day":"01","doi":"10.1142/s0129055x20600120","publisher":"World Scientific Publishing","type":"journal_article","ec_funded":1,"citation":{"short":"R. Seiringer, Reviews in Mathematical Physics 33 (2021).","apa":"Seiringer, R. (2021). The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x20600120\">https://doi.org/10.1142/s0129055x20600120</a>","mla":"Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/s0129055x20600120\">10.1142/s0129055x20600120</a>.","ista":"Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012.","ieee":"R. Seiringer, “The polaron at strong coupling,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.","ama":"Seiringer R. The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>. 2021;33(01). doi:<a href=\"https://doi.org/10.1142/s0129055x20600120\">10.1142/s0129055x20600120</a>","chicago":"Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/s0129055x20600120\">https://doi.org/10.1142/s0129055x20600120</a>."},"volume":33,"date_created":"2022-03-18T08:11:34Z","department":[{"_id":"RoSe"}],"article_number":"2060012","date_updated":"2025-04-14T07:26:58Z","corr_author":"1","external_id":{"arxiv":["1912.12509"],"isi":["000613313200013"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        33","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"month":"02","article_processing_charge":"No","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"title":"The polaron at strong coupling","issue":"01","_id":"10852","year":"2021","oa_version":"Preprint","isi":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"publication_status":"published","article_type":"original","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"author":[{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"arxiv":1,"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).","date_published":"2021-02-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"scopus_import":"1","status":"public"},{"date_updated":"2025-04-14T09:11:09Z","has_accepted_license":"1","external_id":{"arxiv":["2101.12566"],"isi":["000710850600001"]},"intvolume":"       242","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"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)"},"date_created":"2021-11-07T23:01:26Z","file_date_updated":"2021-12-14T08:35:42Z","department":[{"_id":"RoSe"}],"page":"1835–1906","doi":"10.1007/s00205-021-01715-7","publisher":"Springer Nature","day":"25","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9787"}]},"type":"journal_article","ec_funded":1,"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.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2021). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01715-7\">https://doi.org/10.1007/s00205-021-01715-7</a>","mla":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906, doi:<a href=\"https://doi.org/10.1007/s00205-021-01715-7\">10.1007/s00205-021-01715-7</a>.","ieee":"D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” <i>Archive for Rational Mechanics and Analysis</i>, 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.","chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01715-7\">https://doi.org/10.1007/s00205-021-01715-7</a>.","ama":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. <i>Archive for Rational Mechanics and Analysis</i>. 2021;242(3):1835–1906. doi:<a href=\"https://doi.org/10.1007/s00205-021-01715-7\">10.1007/s00205-021-01715-7</a>"},"volume":242,"publication":"Archive for Rational Mechanics and Analysis","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).","ddc":["530"],"arxiv":1,"scopus_import":"1","abstract":[{"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.","lang":"eng"}],"date_published":"2021-10-25T00:00:00Z","status":"public","file":[{"creator":"alisjak","date_created":"2021-12-14T08:35:42Z","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":990529,"file_id":"10544","checksum":"672e9c21b20f1a50854b7c821edbb92f","success":1,"file_name":"2021_Springer_Feliciangeli.pdf","date_updated":"2021-12-14T08:35:42Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"oa":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"publication_status":"published","article_type":"original","author":[{"last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","first_name":"Dario","full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics","year":"2021","issue":"3","_id":"10224","oa_version":"Published Version","month":"10","article_processing_charge":"Yes (via OA deal)"}]