[{"publication_identifier":{"issn":["0022-1236"],"eissn":["1096--0783"]},"language":[{"iso":"eng"}],"oa":1,"article_type":"original","ec_funded":1,"article_number":"110320","publication":"Journal of Functional Analysis","day":"24","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1016/j.jfa.2024.110320","title":"Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion","main_file_link":[{"url":"https://doi.org/10.1016/j.jfa.2024.110320","open_access":"1"}],"year":"2024","arxiv":1,"department":[{"_id":"RoSe"}],"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"acknowledgement":"A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","citation":{"ama":"Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. 2024;286(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>","ista":"Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.","short":"A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024).","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, 110320, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>.","chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>","ieee":"A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” <i>Journal of Functional Analysis</i>, vol. 286, no. 7. Elsevier, 2024."},"publisher":"Elsevier","article_processing_charge":"Yes (in subscription journal)","type":"journal_article","month":"01","status":"public","date_updated":"2024-02-05T12:53:21Z","oa_version":"Published Version","abstract":[{"text":"We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15].","lang":"eng"}],"publication_status":"epub_ahead","date_created":"2024-02-04T23:00:53Z","external_id":{"arxiv":["2301.04894"]},"scopus_import":"1","intvolume":"       286","date_published":"2024-01-24T00:00:00Z","volume":286,"author":[{"orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"_id":"14931","issue":"7","quality_controlled":"1"},{"type":"journal_article","article_processing_charge":"No","citation":{"chicago":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>.","ieee":"C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 1505–1560, 2023.","apa":"Boccato, C., &#38; Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>","ama":"Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. 2023;24:1505-1560. doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>","ista":"Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560.","short":"C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560.","mla":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>."},"publisher":"Springer Nature","date_updated":"2023-08-16T11:34:03Z","oa_version":"Preprint","isi":1,"month":"05","status":"public","scopus_import":"1","publication_status":"published","external_id":{"arxiv":["2205.15284"],"isi":["000910751800002"]},"date_created":"2023-01-15T23:00:52Z","abstract":[{"text":"We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit.","lang":"eng"}],"quality_controlled":"1","_id":"12183","intvolume":"        24","date_published":"2023-05-01T00:00:00Z","volume":24,"page":"1505-1560","author":[{"full_name":"Boccato, Chiara","first_name":"Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","last_name":"Boccato"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"ec_funded":1,"article_type":"original","oa":1,"publication_identifier":{"issn":["1424-0637"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00023-022-01252-3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Annales Henri Poincare","day":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2205.15284"}],"title":"The Bose Gas in a box with Neumann boundary conditions","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged.","year":"2023","arxiv":1,"department":[{"_id":"RoSe"}]},{"day":"15","publication":"Journal of Functional Analysis","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1016/j.jfa.2023.109963","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"oa":1,"ec_funded":1,"article_type":"original","article_number":"109963","arxiv":1,"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"year":"2023","acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":" F06504","call_identifier":"FWF"}],"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9792"}]},"month":"08","status":"public","isi":1,"oa_version":"Preprint","date_updated":"2023-11-14T13:21:01Z","publisher":"Elsevier","citation":{"short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>."},"article_processing_charge":"No","type":"journal_article","author":[{"last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"first_name":"Augusto","full_name":"Gerolin, Augusto","last_name":"Gerolin"},{"full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale"}],"volume":285,"intvolume":"       285","date_published":"2023-08-15T00:00:00Z","_id":"12911","issue":"4","quality_controlled":"1","abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"publication_status":"published","date_created":"2023-05-07T22:01:02Z","scopus_import":"1"},{"doi":"10.1017/fms.2023.45","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication":"Forum of Mathematics","day":"13","ec_funded":1,"article_type":"original","oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2050-5094"]},"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"acknowledgement":"This research was supported by 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.).","year":"2023","department":[{"_id":"RoSe"}],"arxiv":1,"title":"Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron","date_updated":"2023-11-02T12:30:50Z","oa_version":"Published Version","ddc":["500"],"isi":1,"month":"06","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file":[{"checksum":"f672eb7dd015c472c9a04f1b9bf9df7d","creator":"alisjak","date_created":"2023-07-03T10:36:25Z","access_level":"open_access","file_id":"13186","relation":"main_file","file_name":"2023_ForumofMathematics.Sigma_Mitrouskas.pdf","success":1,"file_size":943192,"date_updated":"2023-07-03T10:36:25Z","content_type":"application/pdf"}],"type":"journal_article","article_processing_charge":"Yes","citation":{"ama":"Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. <i>Forum of Mathematics</i>. 2023;11:1-52. doi:<a href=\"https://doi.org/10.1017/fms.2023.45\">10.1017/fms.2023.45</a>","ista":"Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 11, 1–52.","mla":"Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” <i>Forum of Mathematics</i>, vol. 11, Cambridge University Press, 2023, pp. 1–52, doi:<a href=\"https://doi.org/10.1017/fms.2023.45\">10.1017/fms.2023.45</a>.","short":"D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023) 1–52.","chicago":"Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” <i>Forum of Mathematics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.45\">https://doi.org/10.1017/fms.2023.45</a>.","apa":"Mitrouskas, D. J., Mysliwy, K., &#38; Seiringer, R. (2023). Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. <i>Forum of Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.45\">https://doi.org/10.1017/fms.2023.45</a>","ieee":"D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron,” <i>Forum of Mathematics</i>, vol. 11. Cambridge University Press, pp. 1–52, 2023."},"has_accepted_license":"1","publisher":"Cambridge University Press","license":"https://creativecommons.org/licenses/by/4.0/","quality_controlled":"1","_id":"13178","intvolume":"        11","date_published":"2023-06-13T00:00:00Z","author":[{"last_name":"Mitrouskas","first_name":"David Johannes","full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"last_name":"Mysliwy","first_name":"Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","full_name":"Mysliwy, Krzysztof"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"page":"1-52","volume":11,"scopus_import":"1","date_created":"2023-07-02T22:00:43Z","publication_status":"published","external_id":{"isi":["001005008800001"],"arxiv":["2203.02454"]},"file_date_updated":"2023-07-03T10:36:25Z","abstract":[{"text":"We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.","lang":"eng"}]},{"publication_status":"published","date_created":"2023-07-10T16:35:45Z","external_id":{"isi":["000997933500008"],"arxiv":["2201.08090"]},"file_date_updated":"2023-07-11T08:19:15Z","abstract":[{"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.","lang":"eng"}],"date_published":"2023-05-18T00:00:00Z","intvolume":"        12","volume":12,"page":"1507–1540","author":[{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"last_name":"Roos","full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","first_name":"Barbara"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"issue":"4","quality_controlled":"1","_id":"13207","article_processing_charge":"No","citation":{"ista":"Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 12(4), 1507–1540.","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>","short":"C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 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>.","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>.","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.","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>"},"has_accepted_license":"1","publisher":"EMS Press","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"id":"14374","relation":"dissertation_contains","status":"public"}]},"file":[{"file_id":"13208","access_level":"open_access","date_created":"2023-07-11T08:19:15Z","creator":"alisjak","checksum":"5501da33be010b5c81440438287584d5","date_updated":"2023-07-11T08:19:15Z","content_type":"application/pdf","file_size":304619,"success":1,"file_name":"2023_EMS_Hainzl.pdf","relation":"main_file"}],"date_updated":"2023-10-27T10:37:29Z","oa_version":"Published Version","ddc":["530"],"isi":1,"status":"public","month":"05","title":"Boundary superconductivity in the BCS model","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"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.","year":"2023","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"arxiv":1,"oa":1,"publication_identifier":{"issn":["1664-039X"],"eissn":["1664-0403"]},"language":[{"iso":"eng"}],"article_type":"original","ec_funded":1,"publication":"Journal of Spectral Theory","day":"18","doi":"10.4171/JST/439","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"arxiv":1,"department":[{"_id":"RoSe"}],"year":"2023","acknowledgement":"RS was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). MP acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement.","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"title":"Correlation energy of a weakly interacting Fermi gas with large interaction potential","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00205-023-01893-6","day":"01","publication":"Archive for Rational Mechanics and Analysis","ec_funded":1,"article_type":"original","article_number":"65","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"oa":1,"_id":"13225","quality_controlled":"1","issue":"4","volume":247,"author":[{"last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","first_name":"Niels P"},{"full_name":"Porta, Marcello","first_name":"Marcello","last_name":"Porta"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"intvolume":"       247","date_published":"2023-08-01T00:00:00Z","scopus_import":"1","file_date_updated":"2023-11-14T13:12:12Z","abstract":[{"lang":"eng","text":"Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy."}],"publication_status":"published","external_id":{"arxiv":["2106.13185"],"isi":["001024369000001"]},"date_created":"2023-07-16T22:01:08Z","month":"08","status":"public","isi":1,"ddc":["510"],"oa_version":"Published Version","date_updated":"2023-12-13T11:31:14Z","file":[{"creator":"dernst","checksum":"2b45828d854a253b14bf7aa196ec55e9","access_level":"open_access","date_created":"2023-11-14T13:12:12Z","file_id":"14535","relation":"main_file","file_name":"2023_ArchiveRationalMechAnalysis_Benedikter.pdf","date_updated":"2023-11-14T13:12:12Z","content_type":"application/pdf","success":1,"file_size":851626}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","has_accepted_license":"1","publisher":"Springer Nature","citation":{"chicago":"Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>.","apa":"Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>","ieee":"N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4. Springer Nature, 2023.","ista":"Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 247(4), 65.","ama":"Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(4). doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>.","short":"N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023)."},"article_processing_charge":"Yes (via OA deal)"},{"title":"Boundary superconductivity in BCS theory","alternative_title":["ISTA Thesis"],"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"year":"2023","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"publication_identifier":{"issn":["2663 - 337X"]},"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"degree_awarded":"PhD","supervisor":[{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"day":"30","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.15479/at:ista:14374","file_date_updated":"2023-10-06T11:38:01Z","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_created":"2023-09-28T14:23:04Z","publication_status":"published","author":[{"last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","first_name":"Barbara"}],"page":"206","date_published":"2023-09-30T00:00:00Z","_id":"14374","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","publisher":"Institute of Science and Technology Austria","has_accepted_license":"1","citation":{"short":"B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023.","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>.","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>","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>","ieee":"B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023.","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>."},"article_processing_charge":"No","type":"dissertation","file":[{"file_name":"phd-thesis-draft_pdfa_acrobat.pdf","date_updated":"2023-10-06T11:35:56Z","content_type":"application/pdf","file_size":2365702,"relation":"main_file","file_id":"14398","checksum":"ef039ffc3de2cb8dee5b14110938e9b6","creator":"broos","access_level":"open_access","date_created":"2023-10-06T11:35:56Z"},{"access_level":"closed","date_created":"2023-10-06T11:38:01Z","creator":"broos","checksum":"81dcac33daeefaf0111db52f41bb1fd0","file_id":"14399","relation":"source_file","date_updated":"2023-10-06T11:38:01Z","content_type":"application/x-zip-compressed","file_size":4691734,"file_name":"Version5.zip"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"13207"},{"status":"public","id":"10850","relation":"part_of_dissertation"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"month":"09","status":"public","ddc":["515","539"],"oa_version":"Published Version","date_updated":"2023-10-27T10:37:30Z"},{"ec_funded":1,"article_type":"original","oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"doi":"10.1007/s00220-023-04841-3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","publication":"Communications in Mathematical Physics","title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"arxiv":1,"department":[{"_id":"RoSe"}],"year":"2023","type":"journal_article","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","has_accepted_license":"1","citation":{"ieee":"M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 287–337, 2023.","apa":"Brooks, M., &#38; Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>","chicago":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>.","mla":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 287–337, doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>.","short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","ama":"Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. 2023;404:287-337. doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>","ista":"Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337."},"oa_version":"Published Version","date_updated":"2023-10-31T12:22:51Z","status":"public","month":"11","ddc":["510"],"file":[{"relation":"main_file","file_name":"2023_CommMathPhysics_Brooks.pdf","date_updated":"2023-10-31T12:21:39Z","content_type":"application/pdf","file_size":832375,"success":1,"checksum":"1ae49b39247cb6b40ff75997381581b8","creator":"dernst","access_level":"open_access","date_created":"2023-10-31T12:21:39Z","file_id":"14477"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"scopus_import":"1","external_id":{"arxiv":["2207.03156"]},"date_created":"2023-10-22T22:01:13Z","publication_status":"published","file_date_updated":"2023-10-31T12:21:39Z","abstract":[{"text":"We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.","lang":"eng"}],"quality_controlled":"1","_id":"14441","volume":404,"page":"287-337","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","orcid":"0000-0002-6249-0928","first_name":"Morris","full_name":"Brooks, Morris","last_name":"Brooks"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert"}],"intvolume":"       404","date_published":"2023-11-01T00:00:00Z"},{"quality_controlled":"1","issue":"5","_id":"12246","intvolume":"       112","date_published":"2022-09-15T00:00:00Z","author":[{"first_name":"Mathieu","full_name":"Lewin, Mathieu","last_name":"Lewin"},{"full_name":"Lieb, Elliott H.","first_name":"Elliott H.","last_name":"Lieb"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert"}],"volume":112,"scopus_import":"1","date_created":"2023-01-16T09:53:54Z","external_id":{"arxiv":["2203.12473"],"isi":["000854762600001"]},"publication_status":"published","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_updated":"2023-09-05T15:17:34Z","oa_version":"Preprint","isi":1,"month":"09","status":"public","type":"journal_article","article_processing_charge":"No","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>","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>.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).","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>.","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>","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."},"publisher":"Springer Nature","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"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.","year":"2022","department":[{"_id":"RoSe"}],"arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.12473","open_access":"1"}],"title":"Improved Lieb–Oxford bound on the indirect and exchange energies","doi":"10.1007/s11005-022-01584-5","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication":"Letters in Mathematical Physics","day":"15","article_number":"92","ec_funded":1,"article_type":"original","oa":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]}},{"abstract":[{"lang":"eng","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"}],"file_date_updated":"2023-01-26T10:02:42Z","date_created":"2023-01-26T10:00:42Z","publication_status":"published","page":"196","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","first_name":"Morris","orcid":"0000-0002-6249-0928","last_name":"Brooks"}],"date_published":"2022-12-15T00:00:00Z","_id":"12390","publisher":"Institute of Science and Technology Austria","has_accepted_license":"1","citation":{"ieee":"M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022.","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>","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>.","short":"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>.","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>"},"article_processing_charge":"No","type":"dissertation","file":[{"content_type":"application/pdf","date_updated":"2023-01-26T10:02:34Z","success":1,"file_size":3095225,"file_name":"Brooks_Thesis.pdf","relation":"main_file","file_id":"12391","access_level":"open_access","date_created":"2023-01-26T10:02:34Z","checksum":"b31460e937f33b557abb40ebef02b567","creator":"cchlebak"},{"file_id":"12392","date_created":"2023-01-26T10:02:42Z","access_level":"closed","checksum":"9751869fa5e7981588ad4228f4fd4bd6","creator":"cchlebak","file_size":809842,"content_type":"application/octet-stream","date_updated":"2023-01-26T10:02:42Z","file_name":"Brooks_Thesis.tex","relation":"source_file"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"related_material":{"record":[{"id":"9005","relation":"part_of_dissertation","status":"public"}]},"status":"public","month":"12","ddc":["500"],"oa_version":"Published Version","date_updated":"2023-08-07T13:32:09Z","title":"Translation-invariant quantum systems with effectively broken symmetry","alternative_title":["ISTA Thesis"],"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"year":"2022","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"oa":1,"ec_funded":1,"degree_awarded":"PhD","supervisor":[{"last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"day":"15","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.15479/at:ista:12390"},{"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"article_type":"original","article_number":"5","publication":"Journal of Statistical Physics","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s10955-021-02851-w","title":"Polaron models with regular interactions at strong coupling","year":"2022","department":[{"_id":"RoSe"}],"arxiv":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"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).","citation":{"ista":"Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5.","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>","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>.","short":"K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).","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>.","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>","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."},"has_accepted_license":"1","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"status":"public","id":"11473","relation":"dissertation_contains"}]},"file":[{"creator":"cchlebak","checksum":"da03f6d293c4b9802091bce9471b1d29","date_created":"2022-02-02T14:24:41Z","access_level":"open_access","file_id":"10716","relation":"main_file","file_name":"2022_JournalStatPhys_Myśliwy.pdf","success":1,"file_size":434957,"date_updated":"2022-02-02T14:24:41Z","content_type":"application/pdf"}],"ddc":["530"],"isi":1,"month":"01","status":"public","date_updated":"2023-09-07T13:43:51Z","oa_version":"Published Version","file_date_updated":"2022-02-02T14:24:41Z","abstract":[{"lang":"eng","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."}],"date_created":"2021-12-19T23:01:32Z","publication_status":"published","external_id":{"arxiv":["2106.09328"],"isi":["000726275600001"]},"scopus_import":"1","date_published":"2022-01-01T00:00:00Z","intvolume":"       186","volume":186,"author":[{"first_name":"Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","full_name":"Mysliwy, Krzysztof","last_name":"Mysliwy"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"_id":"10564","issue":"1","quality_controlled":"1"},{"title":"The effective mass problem for the Landau-Pekar equations","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"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.","year":"2022","arxiv":1,"department":[{"_id":"RoSe"}],"article_number":"015201","article_type":"original","ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"doi":"10.1088/1751-8121/ac3947","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Journal of Physics A: Mathematical and Theoretical","day":"19","scopus_import":"1","external_id":{"arxiv":["2107.03720"]},"date_created":"2022-02-13T23:01:35Z","publication_status":"published","file_date_updated":"2022-02-14T08:20:19Z","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"}],"quality_controlled":"1","issue":"1","_id":"10755","intvolume":"        55","date_published":"2022-01-19T00:00:00Z","volume":55,"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","first_name":"Dario","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli"},{"last_name":"Rademacher","full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","orcid":"0000-0001-5059-4466"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","citation":{"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.","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>","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>.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022).","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>.","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>","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."},"has_accepted_license":"1","publisher":"IOP Publishing","date_updated":"2024-03-06T12:30:44Z","oa_version":"Published Version","ddc":["510"],"month":"01","status":"public","related_material":{"record":[{"status":"public","id":"9791","relation":"earlier_version"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file":[{"access_level":"open_access","date_created":"2022-02-14T08:20:19Z","creator":"dernst","checksum":"0875e562705563053d6dd98fba4d8578","file_id":"10757","relation":"main_file","content_type":"application/pdf","date_updated":"2022-02-14T08:20:19Z","success":1,"file_size":1132380,"file_name":"2022_JournalPhysicsA_Feliciangeli.pdf"}]},{"issue":"12","quality_controlled":"1","_id":"10850","author":[{"last_name":"Roos","full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","orcid":"0000-0002-9071-5880"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert"}],"volume":282,"intvolume":"       282","date_published":"2022-06-15T00:00:00Z","scopus_import":"1","date_created":"2022-03-16T08:41:53Z","publication_status":"published","external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"file_date_updated":"2022-08-02T10:37:55Z","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","date_updated":"2023-10-27T10:37:29Z","status":"public","month":"06","ddc":["510"],"isi":1,"file":[{"relation":"main_file","content_type":"application/pdf","date_updated":"2022-08-02T10:37:55Z","success":1,"file_size":631391,"file_name":"2022_JourFunctionalAnalysis_Roos.pdf","access_level":"open_access","date_created":"2022-08-02T10:37:55Z","creator":"dernst","checksum":"63efcefaa1f2717244ef5407bd564426","file_id":"11720"}],"related_material":{"record":[{"status":"public","id":"14374","relation":"dissertation_contains"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","article_processing_charge":"Yes (via OA deal)","publisher":"Elsevier","has_accepted_license":"1","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>.","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.","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.","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>","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>.","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022)."},"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.","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"arxiv":1,"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"year":"2022","title":"Two-particle bound states at interfaces and corners","doi":"10.1016/j.jfa.2022.109455","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"15","publication":"Journal of Functional Analysis","article_number":"109455","ec_funded":1,"article_type":"original","oa":1,"keyword":["Analysis"],"publication_identifier":{"issn":["0022-1236"]},"language":[{"iso":"eng"}]},{"department":[{"_id":"RoSe"}],"year":"2022","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.","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"title":"Large deviation estimates for weakly interacting bosons","day":"01","publication":"Journal of Statistical Physics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s10955-022-02940-4","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"oa":1,"ec_funded":1,"article_type":"original","article_number":"9","volume":188,"author":[{"orcid":"0000-0001-5059-4466","id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira","last_name":"Rademacher"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"date_published":"2022-07-01T00:00:00Z","intvolume":"       188","_id":"11917","quality_controlled":"1","file_date_updated":"2022-08-18T08:09:00Z","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."}],"publication_status":"published","date_created":"2022-08-18T07:23:26Z","external_id":{"isi":["000805175000001"]},"scopus_import":"1","file":[{"relation":"main_file","file_size":483481,"success":1,"content_type":"application/pdf","date_updated":"2022-08-18T08:09:00Z","file_name":"2022_JournalStatisticalPhysics_Rademacher.pdf","date_created":"2022-08-18T08:09:00Z","access_level":"open_access","creator":"dernst","checksum":"44418cb44f07fa21ed3907f85abf7f39","file_id":"11922"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","month":"07","isi":1,"ddc":["510"],"oa_version":"Published Version","date_updated":"2023-08-03T12:55:58Z","has_accepted_license":"1","publisher":"Springer Nature","citation":{"ista":"Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9.","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>","short":"S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).","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>.","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>.","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.","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>"},"article_processing_charge":"Yes (via OA deal)","type":"journal_article"},{"type":"journal_article","publisher":"AIP Publishing","has_accepted_license":"1","citation":{"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>.","short":"S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022).","ista":"Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 63(8), 081902.","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>","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.","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>."},"article_processing_charge":"No","status":"public","month":"08","isi":1,"ddc":["510"],"oa_version":"Published Version","date_updated":"2023-08-03T13:57:19Z","file":[{"file_id":"12089","checksum":"e6fb0cf3f0327739c5e69a2cfc4020eb","creator":"dernst","date_created":"2022-09-12T07:35:34Z","access_level":"open_access","file_name":"2022_JourMathPhysics_Rademacher.pdf","file_size":4552261,"success":1,"date_updated":"2022-09-12T07:35:34Z","content_type":"application/pdf","relation":"main_file"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"scopus_import":"1","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"}],"file_date_updated":"2022-09-12T07:35:34Z","date_created":"2022-09-11T22:01:56Z","publication_status":"published","external_id":{"arxiv":["2112.04817"],"isi":["000844402500001"]},"_id":"12083","issue":"8","quality_controlled":"1","volume":63,"author":[{"orcid":"0000-0001-5059-4466","first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","last_name":"Rademacher"}],"intvolume":"        63","date_published":"2022-08-25T00:00:00Z","ec_funded":1,"article_type":"original","article_number":"081902","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"]},"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1063/5.0086712","day":"25","publication":"Journal of Mathematical Physics","title":"Dependent random variables in quantum dynamics","arxiv":1,"department":[{"_id":"RoSe"}],"year":"2022","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.","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}]},{"day":"01","publication":"Communications on Pure and Applied Mathematics","doi":"10.1002/cpa.21944","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["10970312"],"issn":["00103640"]},"ec_funded":1,"article_type":"original","acknowledgement":"Partial support through National Science Foundation GrantDMS-1363432 (R.L.F.) and the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo 694227; R.S.), is acknowledged. Open access funding enabled and organizedby Projekt DEAL.","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"department":[{"_id":"RoSe"}],"year":"2021","title":"Quantum corrections to the Pekar asymptotics of a strongly coupled polaron","file":[{"creator":"dernst","checksum":"5f665ffa6e6dd958aec5c3040cbcfa84","date_created":"2021-03-11T10:03:30Z","access_level":"open_access","file_id":"9236","relation":"main_file","file_name":"2021_CommPureApplMath_Frank.pdf","file_size":334987,"success":1,"date_updated":"2021-03-11T10:03:30Z","content_type":"application/pdf"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa_version":"Published Version","date_updated":"2023-08-04T11:02:16Z","month":"03","status":"public","isi":1,"ddc":["510"],"article_processing_charge":"No","has_accepted_license":"1","publisher":"Wiley","citation":{"short":"R. Frank, R. Seiringer, Communications on Pure and Applied Mathematics 74 (2021) 544–588.","mla":"Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” <i>Communications on Pure and Applied Mathematics</i>, vol. 74, no. 3, Wiley, 2021, pp. 544–88, doi:<a href=\"https://doi.org/10.1002/cpa.21944\">10.1002/cpa.21944</a>.","ista":"Frank R, Seiringer R. 2021. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. 74(3), 544–588.","ama":"Frank R, Seiringer R. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. <i>Communications on Pure and Applied Mathematics</i>. 2021;74(3):544-588. doi:<a href=\"https://doi.org/10.1002/cpa.21944\">10.1002/cpa.21944</a>","ieee":"R. Frank and R. Seiringer, “Quantum corrections to the Pekar asymptotics of a strongly coupled polaron,” <i>Communications on Pure and Applied Mathematics</i>, vol. 74, no. 3. Wiley, pp. 544–588, 2021.","apa":"Frank, R., &#38; Seiringer, R. (2021). Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.21944\">https://doi.org/10.1002/cpa.21944</a>","chicago":"Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2021. <a href=\"https://doi.org/10.1002/cpa.21944\">https://doi.org/10.1002/cpa.21944</a>."},"type":"journal_article","author":[{"last_name":"Frank","full_name":"Frank, Rupert","first_name":"Rupert"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"volume":74,"page":"544-588","intvolume":"        74","date_published":"2021-03-01T00:00:00Z","issue":"3","quality_controlled":"1","_id":"8603","date_created":"2020-10-04T22:01:37Z","publication_status":"published","external_id":{"isi":["000572991500001"]},"file_date_updated":"2021-03-11T10:03:30Z","abstract":[{"lang":"eng","text":"We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem."}],"scopus_import":"1"},{"file":[{"creator":"dernst","checksum":"ffbfe1aad623bce7ff529c207e343b53","access_level":"open_access","date_created":"2021-03-09T11:44:34Z","file_id":"9232","relation":"main_file","file_name":"2021_LettersMathPhysics_Feliciangeli.pdf","date_updated":"2021-03-09T11:44:34Z","content_type":"application/pdf","file_size":391205,"success":1}],"related_material":{"record":[{"status":"public","id":"9733","relation":"dissertation_contains"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"month":"02","status":"public","ddc":["510"],"isi":1,"oa_version":"Published Version","date_updated":"2023-09-07T13:30:11Z","publisher":"Springer Nature","has_accepted_license":"1","citation":{"ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the spectral gap for the Landau–Pekar equations,” <i>Letters in Mathematical Physics</i>, vol. 111. Springer Nature, 2021.","apa":"Feliciangeli, D., Rademacher, S. A. E., &#38; Seiringer, R. (2021). Persistence of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01350-5\">https://doi.org/10.1007/s11005-020-01350-5</a>","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11005-020-01350-5\">https://doi.org/10.1007/s11005-020-01350-5</a>.","mla":"Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” <i>Letters in Mathematical Physics</i>, vol. 111, 19, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11005-020-01350-5\">10.1007/s11005-020-01350-5</a>.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical Physics 111 (2021).","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19.","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap for the Landau–Pekar equations. <i>Letters in Mathematical Physics</i>. 2021;111. doi:<a href=\"https://doi.org/10.1007/s11005-020-01350-5\">10.1007/s11005-020-01350-5</a>"},"article_processing_charge":"Yes (via OA deal)","type":"journal_article","volume":111,"author":[{"full_name":"Feliciangeli, Dario","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"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"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"intvolume":"       111","date_published":"2021-02-11T00:00:00Z","_id":"9225","quality_controlled":"1","file_date_updated":"2021-03-09T11:44:34Z","abstract":[{"text":"The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere, we provide a class of initial data for which the associated effective Hamiltonian\r\nhas a uniform spectral gap for all times. For such initial data, this allows us to extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations and their derivation\r\nfrom the Fröhlich model obtained in previous works to larger times.","lang":"eng"}],"external_id":{"isi":["000617195700001"]},"date_created":"2021-03-07T23:01:25Z","publication_status":"published","scopus_import":"1","day":"11","publication":"Letters in Mathematical Physics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s11005-020-01350-5","publication_identifier":{"eissn":["15730530"],"issn":["03779017"]},"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"article_type":"original","article_number":"19","department":[{"_id":"RoSe"}],"year":"2021","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged. Open Access funding provided by Institute of Science and Technology (IST Austria)","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"title":"Persistence of the spectral gap for the Landau–Pekar equations"},{"scopus_import":"1","date_created":"2021-03-14T23:01:34Z","external_id":{"arxiv":["2001.03993"],"isi":["000622226200001"]},"publication_status":"published","abstract":[{"text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.","lang":"eng"}],"file_date_updated":"2021-03-22T08:31:29Z","quality_controlled":"1","_id":"9246","page":"383-417","author":[{"first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","last_name":"Leopold"},{"last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes","full_name":"Mitrouskas, David Johannes"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"volume":240,"date_published":"2021-02-26T00:00:00Z","intvolume":"       240","type":"journal_article","article_processing_charge":"No","publisher":"Springer Nature","has_accepted_license":"1","citation":{"chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>.","apa":"Leopold, N. K., Mitrouskas, D. J., &#38; Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240. Springer Nature, pp. 383–417, 2021.","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. 2021;240:383-417. doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>","mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240, Springer Nature, 2021, pp. 383–417, doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>.","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417."},"oa_version":"Published Version","date_updated":"2023-08-07T14:12:27Z","month":"02","status":"public","isi":1,"ddc":["510"],"file":[{"file_name":"2021_ArchRationalMechAnal_Leopold.pdf","file_size":558006,"success":1,"content_type":"application/pdf","date_updated":"2021-03-22T08:31:29Z","relation":"main_file","file_id":"9270","checksum":"23449e44dc5132501a5c86e70638800f","creator":"dernst","date_created":"2021-03-22T08:31:29Z","access_level":"open_access"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"department":[{"_id":"RoSe"}],"arxiv":1,"year":"2021","article_type":"original","ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320673"],"issn":["00039527"]},"doi":"10.1007/s00205-021-01616-9","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"26","publication":"Archive for Rational Mechanics and Analysis"},{"_id":"9318","quality_controlled":"1","volume":9,"author":[{"first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann"},{"last_name":"Petrat","first_name":"Sören P","full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"}],"intvolume":"         9","date_published":"2021-03-26T00:00:00Z","scopus_import":"1","abstract":[{"text":"We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.","lang":"eng"}],"file_date_updated":"2021-04-12T07:15:58Z","publication_status":"published","date_created":"2021-04-11T22:01:15Z","external_id":{"isi":["000634006900001"]},"status":"public","month":"03","ddc":["510"],"isi":1,"oa_version":"Published Version","date_updated":"2023-08-07T14:35:06Z","file":[{"relation":"main_file","file_size":883851,"success":1,"content_type":"application/pdf","date_updated":"2021-04-12T07:15:58Z","file_name":"2021_ForumMath_Bossmann.pdf","date_created":"2021-04-12T07:15:58Z","access_level":"open_access","creator":"dernst","checksum":"17a3e6786d1e930cf0c14a880a6d7e92","file_id":"9319"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","has_accepted_license":"1","publisher":"Cambridge University Press","citation":{"apa":"Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>","ieee":"L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.","chicago":"Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>.","mla":"Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>.","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.","ama":"Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>"},"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"RoSe"}],"year":"2021","acknowledgement":"The first author gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 754411. The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1017/fms.2021.22","day":"26","publication":"Forum of Mathematics, Sigma","ec_funded":1,"article_type":"original","article_number":"e28","publication_identifier":{"eissn":["20505094"]},"language":[{"iso":"eng"}],"oa":1},{"type":"journal_article","publisher":"World Scientific","citation":{"ama":"Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href=\"https://doi.org/10.1142/S0129055X20600065\">10.1142/S0129055X20600065</a>","ista":"Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 33(1), 2060006.","short":"C. Boccato, Reviews in Mathematical Physics 33 (2021).","mla":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060006, World Scientific, 2021, doi:<a href=\"https://doi.org/10.1142/S0129055X20600065\">10.1142/S0129055X20600065</a>.","chicago":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” <i>Reviews in Mathematical Physics</i>. World Scientific, 2021. <a href=\"https://doi.org/10.1142/S0129055X20600065\">https://doi.org/10.1142/S0129055X20600065</a>.","apa":"Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. <i>Reviews in Mathematical Physics</i>. World Scientific. <a href=\"https://doi.org/10.1142/S0129055X20600065\">https://doi.org/10.1142/S0129055X20600065</a>","ieee":"C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021."},"article_processing_charge":"No","month":"01","status":"public","isi":1,"oa_version":"Preprint","date_updated":"2023-08-04T10:50:13Z","scopus_import":"1","abstract":[{"lang":"eng","text":"We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein."}],"external_id":{"arxiv":["2001.00497"],"isi":["000613313200007"]},"publication_status":"published","date_created":"2020-04-26T22:00:45Z","_id":"7685","issue":"1","quality_controlled":"1","author":[{"last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara","full_name":"Boccato, Chiara"}],"volume":33,"date_published":"2021-01-01T00:00:00Z","intvolume":"        33","ec_funded":1,"article_type":"original","article_number":"2060006","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0129-055X"]},"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1142/S0129055X20600065","day":"01","publication":"Reviews in Mathematical Physics","main_file_link":[{"url":"https://arxiv.org/abs/2001.00497","open_access":"1"}],"title":"The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime","department":[{"_id":"RoSe"}],"arxiv":1,"year":"2021","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}]}]