[{"OA_type":"hybrid","ec_funded":1,"title":"Virtual bound states of the Pauli operator with an Aharonov–Bohm potential","publication_status":"published","has_accepted_license":"1","abstract":[{"text":"A maximal realization of the two-dimensional Pauli operator, subject to Aharonov–Bohm magnetic field, is investigated. Contrary to the case of the Pauli operator with regular magnetic potentials, it is shown that both components of the Pauli operator are critical. Asymptotics of the weakly coupled eigenvalues, generated by electric (not necessarily self-adjoint) perturbations, are derived.","lang":"eng"}],"intvolume":"        37","OA_place":"publisher","publication":"Reviews in Mathematical Physics","quality_controlled":"1","day":"01","acknowledgement":"Thanks belong to Johannes Ageskov and Matˇej Tuˇsek for helpful discussions on some technical details. M. F. would further like to acknowledge support for research on this paper from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101034413 as well as support by funding from Villum Fonden through the QMATH Centreof Excellence Grant No. 10059. D. K. was supported by the EXPRO Grant No.20-17749X of the Czech Science Foundation (GACR).","arxiv":1,"oa":1,"article_processing_charge":"Yes (in subscription journal)","isi":1,"citation":{"mla":"Fialova, Marie, and David Krejčiřík. “Virtual Bound States of the Pauli Operator with an Aharonov–Bohm Potential.” <i>Reviews in Mathematical Physics</i>, vol. 37, no. 6, 2550011, World Scientific Publishing, 2025, doi:<a href=\"https://doi.org/10.1142/S0129055X25500114\">10.1142/S0129055X25500114</a>.","ieee":"M. Fialova and D. Krejčiřík, “Virtual bound states of the Pauli operator with an Aharonov–Bohm potential,” <i>Reviews in Mathematical Physics</i>, vol. 37, no. 6. World Scientific Publishing, 2025.","short":"M. Fialova, D. Krejčiřík, Reviews in Mathematical Physics 37 (2025).","apa":"Fialova, M., &#38; Krejčiřík, D. (2025). Virtual bound states of the Pauli operator with an Aharonov–Bohm potential. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X25500114\">https://doi.org/10.1142/S0129055X25500114</a>","ama":"Fialova M, Krejčiřík D. Virtual bound states of the Pauli operator with an Aharonov–Bohm potential. <i>Reviews in Mathematical Physics</i>. 2025;37(6). doi:<a href=\"https://doi.org/10.1142/S0129055X25500114\">10.1142/S0129055X25500114</a>","ista":"Fialova M, Krejčiřík D. 2025. Virtual bound states of the Pauli operator with an Aharonov–Bohm potential. Reviews in Mathematical Physics. 37(6), 2550011.","chicago":"Fialova, Marie, and David Krejčiřík. “Virtual Bound States of the Pauli Operator with an Aharonov–Bohm Potential.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2025. <a href=\"https://doi.org/10.1142/S0129055X25500114\">https://doi.org/10.1142/S0129055X25500114</a>."},"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"language":[{"iso":"eng"}],"author":[{"last_name":"Fialova","first_name":"Marie","id":"e9c9844d-9e21-11ec-b482-f96fc09f7c4d","full_name":"Fialova, Marie"},{"full_name":"Krejčiřík, David","first_name":"David","last_name":"Krejčiřík"}],"scopus_import":"1","month":"07","volume":37,"publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"doi":"10.1142/S0129055X25500114","PlanS_conform":"1","file":[{"relation":"main_file","date_created":"2025-12-30T08:23:12Z","success":1,"content_type":"application/pdf","access_level":"open_access","date_updated":"2025-12-30T08:23:12Z","checksum":"559d97ee2da28bf0bd2c6af507f3a914","file_size":484646,"file_name":"2025_ReviewsMathPhysics_Fialova.pdf","file_id":"20893","creator":"dernst"}],"_id":"19705","article_number":"2550011","oa_version":"Published Version","file_date_updated":"2025-12-30T08:23:12Z","department":[{"_id":"RoSe"}],"APC_amount":"2320,48 EUR","date_updated":"2026-05-06T13:03:25Z","external_id":{"isi":["001481012500001"],"arxiv":["2501.17029"]},"date_created":"2025-05-18T22:02:51Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-07-01T00:00:00Z","status":"public","year":"2025","issue":"6","ddc":["530","510"],"publisher":"World Scientific Publishing","article_type":"original","type":"journal_article"},{"day":"01","quality_controlled":"1","intvolume":"        36","abstract":[{"lang":"eng","text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."}],"OA_place":"publisher","publication":"Reviews in Mathematical Physics","corr_author":"1","title":"Universality in low-dimensional BCS theory","publication_status":"published","has_accepted_license":"1","ec_funded":1,"OA_type":"hybrid","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"scopus_import":"1","month":"10","volume":36,"language":[{"iso":"eng"}],"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard"},{"orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara"}],"citation":{"ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2024;36(9). doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2024). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9. World Scientific Publishing, 2024.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>."},"article_processing_charge":"Yes (in subscription journal)","isi":1,"oa":1,"acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","arxiv":1,"external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"date_updated":"2026-07-29T13:18:16Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"18135"},{"status":"public","relation":"dissertation_contains","id":"19540"}]},"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"oa_version":"Published Version","file_date_updated":"2025-01-09T07:56:28Z","file":[{"checksum":"2b053a4223b4db14b90520999ec56054","date_updated":"2025-01-09T07:56:28Z","access_level":"open_access","creator":"dernst","file_id":"18786","file_size":503910,"file_name":"2024_ReviewsmathPhysics_Henheik.pdf","relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2025-01-09T07:56:28Z"}],"_id":"14542","article_number":"2360005 ","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"doi":"10.1142/s0129055x2360005x","publisher":"World Scientific Publishing","article_type":"original","type":"journal_article","issue":"9","ddc":["510"],"year":"2024","date_published":"2024-10-01T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-11-15T23:48:14Z"},{"quality_controlled":"1","day":"09","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2110.00458"}],"publication_status":"published","title":"Bogoliubov dynamics and higher-order corrections for the regularized Nelson model","intvolume":"        35","abstract":[{"text":"We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.","lang":"eng"}],"publication":"Reviews in Mathematical Physics","publication_identifier":{"issn":["0129-055X"]},"scopus_import":"1","month":"01","volume":35,"citation":{"chicago":"Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>.","ista":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 35(4), 2350006.","ama":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. 2023;35(4). doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>","apa":"Falconi, M., Leopold, N. K., Mitrouskas, D. J., &#38; Petrat, S. P. (2023). Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>","short":"M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (2023).","ieee":"M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov dynamics and higher-order corrections for the regularized Nelson model,” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4. World Scientific Publishing, 2023.","mla":"Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4, 2350006, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>."},"article_processing_charge":"No","isi":1,"language":[{"iso":"eng"}],"author":[{"full_name":"Falconi, Marco","first_name":"Marco","last_name":"Falconi"},{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","last_name":"Leopold","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes","last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes"},{"orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P"}],"arxiv":1,"oa":1,"date_updated":"2023-08-16T11:47:27Z","external_id":{"isi":["000909760300001"],"arxiv":["2110.00458"]},"department":[{"_id":"RoSe"}],"_id":"12430","article_number":"2350006","oa_version":"Preprint","doi":"10.1142/S0129055X2350006X","publisher":"World Scientific Publishing","article_type":"original","type":"journal_article","year":"2023","issue":"4","date_published":"2023-01-09T00:00:00Z","status":"public","date_created":"2023-01-29T23:00:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"author":[{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"}],"language":[{"iso":"eng"}],"project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"article_processing_charge":"No","isi":1,"citation":{"mla":"Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/s0129055x20600120\">10.1142/s0129055x20600120</a>.","ieee":"R. Seiringer, “The polaron at strong coupling,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.","short":"R. Seiringer, Reviews in Mathematical Physics 33 (2021).","ama":"Seiringer R. The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>. 2021;33(01). doi:<a href=\"https://doi.org/10.1142/s0129055x20600120\">10.1142/s0129055x20600120</a>","apa":"Seiringer, R. (2021). The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x20600120\">https://doi.org/10.1142/s0129055x20600120</a>","ista":"Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012.","chicago":"Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/s0129055x20600120\">https://doi.org/10.1142/s0129055x20600120</a>."},"oa":1,"arxiv":1,"acknowledgement":"This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227).","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"volume":33,"month":"02","scopus_import":"1","publication":"Reviews in Mathematical Physics","intvolume":"        33","abstract":[{"text":" We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.","lang":"eng"}],"title":"The polaron at strong coupling","publication_status":"published","corr_author":"1","ec_funded":1,"day":"01","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1912.12509","open_access":"1"}],"status":"public","date_published":"2021-02-01T00:00:00Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2022-03-18T08:11:34Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_type":"original","type":"journal_article","publisher":"World Scientific Publishing","issue":"01","year":"2021","oa_version":"Preprint","_id":"10852","article_number":"2060012","doi":"10.1142/s0129055x20600120","external_id":{"isi":["000613313200013"],"arxiv":["1912.12509"]},"date_updated":"2025-04-14T07:26:58Z","department":[{"_id":"RoSe"}]},{"citation":{"ista":"Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 33(1), 2060006.","chicago":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 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 Publishing. <a href=\"https://doi.org/10.1142/S0129055X20600065\">https://doi.org/10.1142/S0129055X20600065</a>","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>","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 Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/S0129055X20600065\">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 Publishing, 2021."},"isi":1,"article_processing_charge":"No","author":[{"full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara","last_name":"Boccato"}],"language":[{"iso":"eng"}],"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"arxiv":1,"oa":1,"publication_identifier":{"issn":["0129-055X"]},"volume":33,"scopus_import":"1","month":"01","publication_status":"published","title":"The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime","publication":"Reviews in Mathematical Physics","abstract":[{"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.","lang":"eng"}],"intvolume":"        33","ec_funded":1,"quality_controlled":"1","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/2001.00497","open_access":"1"}],"status":"public","date_published":"2021-01-01T00:00:00Z","date_created":"2020-04-26T22:00:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_type":"original","publisher":"World Scientific Publishing","year":"2021","issue":"1","_id":"7685","article_number":"2060006","oa_version":"Preprint","doi":"10.1142/S0129055X20600065","date_updated":"2025-05-14T10:49:57Z","external_id":{"isi":["000613313200007"],"arxiv":["2001.00497"]},"department":[{"_id":"RoSe"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-05-28T16:47:55Z","date_published":"2021-01-01T00:00:00Z","status":"public","issue":"1","year":"2021","publisher":"World Scientific Publishing","article_type":"original","type":"journal_article","doi":"10.1142/s0129055x20600090","oa_version":"Preprint","_id":"7900","article_number":"2060009","department":[{"_id":"RoSe"}],"external_id":{"arxiv":["1910.08190"],"isi":["000613313200010"]},"date_updated":"2025-05-14T10:49:46Z","oa":1,"arxiv":1,"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","first_name":"Niels P"}],"article_processing_charge":"No","citation":{"short":"N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).","ama":"Benedikter NP. Bosonic collective excitations in Fermi gases. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href=\"https://doi.org/10.1142/s0129055x20600090\">10.1142/s0129055x20600090</a>","apa":"Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x20600090\">https://doi.org/10.1142/s0129055x20600090</a>","ista":"Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 33(1), 2060009.","chicago":"Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/s0129055x20600090\">https://doi.org/10.1142/s0129055x20600090</a>.","ieee":"N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific Publishing, 2021.","mla":"Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060009, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/s0129055x20600090\">10.1142/s0129055x20600090</a>."},"isi":1,"month":"01","scopus_import":"1","volume":33,"publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"ec_funded":1,"intvolume":"        33","abstract":[{"lang":"eng","text":"Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation."}],"publication":"Reviews in Mathematical Physics","publication_status":"published","title":"Bosonic collective excitations in Fermi gases","main_file_link":[{"url":"https://arxiv.org/abs/1910.08190","open_access":"1"}],"day":"01","quality_controlled":"1"},{"extern":"1","date_updated":"2023-02-23T13:53:59Z","external_id":{"arxiv":["2002.08669"]},"doi":"10.1142/s0129055x20600041","article_number":"2060004","_id":"9285","oa_version":"Preprint","year":"2021","issue":"01","ddc":["500"],"publisher":"World Scientific Publishing","article_type":"original","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-03-26T11:29:46Z","date_published":"2021-02-01T00:00:00Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.08669"}],"quality_controlled":"1","day":"01","publication_status":"published","title":"Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results","has_accepted_license":"1","abstract":[{"lang":"eng","text":"We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit."}],"intvolume":"        33","publication":"Reviews in Mathematical Physics","scopus_import":"1","month":"02","volume":33,"publication_identifier":{"issn":["0129-055X","1793-6659"]},"arxiv":1,"oa":1,"citation":{"ieee":"S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01, 2060004, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/s0129055x20600041\">10.1142/s0129055x20600041</a>.","short":"S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021).","ama":"Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. <i>Reviews in Mathematical Physics</i>. 2021;33(01). doi:<a href=\"https://doi.org/10.1142/s0129055x20600041\">10.1142/s0129055x20600041</a>","apa":"Henheik, S. J., &#38; Teufel, S. (2021). Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x20600041\">https://doi.org/10.1142/s0129055x20600041</a>","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/s0129055x20600041\">https://doi.org/10.1142/s0129055x20600041</a>.","ista":"Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 33(01), 2060004."},"article_processing_charge":"No","language":[{"iso":"eng"}],"author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}]},{"doi":"10.1142/S0129055X0500242X","OA_type":"closed access","publication":"Reviews in Mathematical Physics","abstract":[{"lang":"eng","text":"We study the long time evolution of a quantum particle interacting with a random potential in the Boltzmann-Grad low density limit. We prove that the phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation. The Boltzmann collision kernel is given by the full quantum scattering cross-section of the obstacle potential."}],"intvolume":"        17","oa_version":"None","publication_status":"published","_id":"2744","title":"The linear Boltzmann equation as the low density limit of a random Schrödinger equation","day":"01","date_updated":"2026-07-29T11:19:15Z","extern":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:59:22Z","publist_id":"4148","author":[{"first_name":"David","last_name":"Eng","full_name":"Eng, David"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"}],"language":[{"iso":"eng"}],"page":"669 - 743","status":"public","date_published":"2005-07-01T00:00:00Z","article_processing_charge":"No","citation":{"mla":"Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.” <i>Reviews in Mathematical Physics</i>, vol. 17, no. 6, World Scientific Publishing, 2005, pp. 669–743, doi:<a href=\"https://doi.org/10.1142/S0129055X0500242X\">10.1142/S0129055X0500242X</a>.","ieee":"D. Eng and L. Erdös, “The linear Boltzmann equation as the low density limit of a random Schrödinger equation,” <i>Reviews in Mathematical Physics</i>, vol. 17, no. 6. World Scientific Publishing, pp. 669–743, 2005.","short":"D. Eng, L. Erdös, Reviews in Mathematical Physics 17 (2005) 669–743.","chicago":"Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2005. <a href=\"https://doi.org/10.1142/S0129055X0500242X\">https://doi.org/10.1142/S0129055X0500242X</a>.","ista":"Eng D, Erdös L. 2005. The linear Boltzmann equation as the low density limit of a random Schrödinger equation. Reviews in Mathematical Physics. 17(6), 669–743.","ama":"Eng D, Erdös L. The linear Boltzmann equation as the low density limit of a random Schrödinger equation. <i>Reviews in Mathematical Physics</i>. 2005;17(6):669-743. doi:<a href=\"https://doi.org/10.1142/S0129055X0500242X\">10.1142/S0129055X0500242X</a>","apa":"Eng, D., &#38; Erdös, L. (2005). The linear Boltzmann equation as the low density limit of a random Schrödinger equation. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X0500242X\">https://doi.org/10.1142/S0129055X0500242X</a>"},"issue":"6","year":"2005","volume":17,"month":"07","article_type":"original","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"type":"journal_article","publisher":"World Scientific Publishing"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/math-ph/0001036"}],"quality_controlled":"1","day":"01","title":"The kernel of Dirac operators on S3 and R3","publication_status":"published","abstract":[{"text":"In this paper we describe an intrinsically geometric way of producing magnetic fields on S3 and R3 for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are able to compute the dimension of the kernel. In particular we can give examples where the kernel has any given dimension. This generalizes the examples of Loss and Yau [1].","lang":"eng"}],"intvolume":"        13","publication":"Reviews in Mathematical Physics","month":"10","scopus_import":"1","volume":13,"publication_identifier":{"issn":["0129-055X"]},"arxiv":1,"publist_id":"4158","oa":1,"citation":{"ieee":"L. Erdös and J. Solovej, “The kernel of Dirac operators on S3 and R3,” <i>Reviews in Mathematical Physics</i>, vol. 13, no. 10. World Scientific Publishing, pp. 1247–1280, 2001.","mla":"Erdös, László, and Jan Solovej. “The Kernel of Dirac Operators on S3 and R3.” <i>Reviews in Mathematical Physics</i>, vol. 13, no. 10, World Scientific Publishing, 2001, pp. 1247–80, doi:<a href=\"https://doi.org/10.1142/S0129055X01000983\">10.1142/S0129055X01000983</a>.","short":"L. Erdös, J. Solovej, Reviews in Mathematical Physics 13 (2001) 1247–1280.","chicago":"Erdös, László, and Jan Solovej. “The Kernel of Dirac Operators on S3 and R3.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2001. <a href=\"https://doi.org/10.1142/S0129055X01000983\">https://doi.org/10.1142/S0129055X01000983</a>.","ista":"Erdös L, Solovej J. 2001. The kernel of Dirac operators on S3 and R3. Reviews in Mathematical Physics. 13(10), 1247–1280.","apa":"Erdös, L., &#38; Solovej, J. (2001). The kernel of Dirac operators on S3 and R3. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X01000983\">https://doi.org/10.1142/S0129055X01000983</a>","ama":"Erdös L, Solovej J. The kernel of Dirac operators on S3 and R3. <i>Reviews in Mathematical Physics</i>. 2001;13(10):1247-1280. doi:<a href=\"https://doi.org/10.1142/S0129055X01000983\">10.1142/S0129055X01000983</a>"},"article_processing_charge":"No","page":"1247 - 1280","language":[{"iso":"eng"}],"author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"extern":"1","date_updated":"2023-05-16T12:24:25Z","external_id":{"arxiv":["math-ph/0001036"]},"doi":"10.1142/S0129055X01000983","_id":"2734","oa_version":"Published Version","year":"2001","issue":"10","publisher":"World Scientific Publishing","article_type":"original","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_created":"2018-12-11T11:59:19Z","date_published":"2001-10-01T00:00:00Z","status":"public"}]