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Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.","lang":"eng"}],"date_created":"2025-03-16T23:01:24Z","publication":"Archive for Rational Mechanics and Analysis","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"arxiv":1,"language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","month":"04","corr_author":"1","publication_status":"published","department":[{"_id":"RoSe"}],"day":"01","doi":"10.1007/s00205-025-02088-x","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","scopus_import":"1","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ieee":"B. Roos and R. Seiringer, “BCS critical temperature on half-spaces,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249. Springer Nature, 2025.","apa":"Roos, B., &#38; Seiringer, R. (2025). BCS critical temperature on half-spaces. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-025-02088-x\">https://doi.org/10.1007/s00205-025-02088-x</a>","ama":"Roos B, Seiringer R. BCS critical temperature on half-spaces. <i>Archive for Rational Mechanics and Analysis</i>. 2025;249. doi:<a href=\"https://doi.org/10.1007/s00205-025-02088-x\">10.1007/s00205-025-02088-x</a>","mla":"Roos, Barbara, and Robert Seiringer. “BCS Critical Temperature on Half-Spaces.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, 20, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00205-025-02088-x\">10.1007/s00205-025-02088-x</a>.","short":"B. Roos, R. Seiringer, Archive for Rational Mechanics and Analysis 249 (2025).","chicago":"Roos, Barbara, and Robert Seiringer. “BCS Critical Temperature on Half-Spaces.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00205-025-02088-x\">https://doi.org/10.1007/s00205-025-02088-x</a>.","ista":"Roos B, Seiringer R. 2025. BCS critical temperature on half-spaces. Archive for Rational Mechanics and Analysis. 249, 20."},"file":[{"date_created":"2025-03-17T10:07:45Z","file_id":"19412","file_name":"2025_ArchiveRatMech_Roos.pdf","date_updated":"2025-03-17T10:07:45Z","creator":"dernst","file_size":1224282,"access_level":"open_access","success":1,"content_type":"application/pdf","checksum":"66803fb63a57987eb4f13ee2949bea77","relation":"main_file"}],"isi":1,"author":[{"last_name":"Roos","full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","first_name":"Barbara"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"external_id":{"pmid":["40041541"],"arxiv":["2306.05824"],"isi":["001435380100001"]},"_id":"19403","volume":249,"intvolume":"       249","article_processing_charge":"Yes (via OA deal)","pmid":1,"date_published":"2025-04-01T00:00:00Z","year":"2025","article_number":"20","project":[{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publisher":"Springer Nature","ddc":["510"]},{"abstract":[{"lang":"eng","text":"We consider the BCS energy gap „.T / (essentially given by „.T / \u0019 .T; p\u0016/,\r\nthe BCS order parameter) at all temperatures 0 \u0014 T \u0014 Tc up to the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio „.T /=Tc is given by a universal function of the relative temperature T =Tc. On the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev. B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors for temperatures bounded uniformly away from Tc. On the other hand, our result lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1; 2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in two dimensions), and treat the perhaps physically most interesting (due to the occurrence of the superconducting phase transition) regime of\r\ntemperatures close to Tc.\r\n\r\n​\r\n ."}],"publication":"Journal of Spectral Theory","date_created":"2025-04-11T09:19:28Z","publication_identifier":{"eissn":["1664-0403"]},"file_date_updated":"2025-04-11T09:13:31Z","DOAJ_listed":"1","type":"journal_article","date_updated":"2026-04-07T12:37:11Z","article_type":"original","OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Universal behavior of the BCS energy gap","OA_type":"gold","has_accepted_license":"1","oa":1,"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ama":"Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. 2025;15(1):305–352. doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>","ieee":"S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,” <i>Journal of Spectral Theory</i>, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.","ista":"Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352."},"file":[{"content_type":"application/pdf","checksum":"f49e06e8dba819f7ad52a202e287ebca","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2025-04-11T09:13:31Z","creator":"cchlebak","file_size":779158,"date_created":"2025-04-11T09:13:31Z","file_id":"19549","file_name":"Henheik_JSpectralTheory_2025.pdf"}],"acknowledgement":"We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin Langmann and Robert Seiringer for valuable comments on an earlier version of the manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n","scopus_import":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"corr_author":"1","month":"01","publication_status":"published","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"ec_funded":1,"day":"09","doi":"10.4171/JST/540","arxiv":1,"oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        15","volume":15,"issue":"1","_id":"19548","external_id":{"arxiv":["2312.11310"],"isi":["001438931600009"]},"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"}],"isi":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publisher":"EMS Press","ddc":["500"],"year":"2025","date_published":"2025-01-09T00:00:00Z","article_processing_charge":"No","page":"305–352"},{"_id":"19628","external_id":{"arxiv":["2308.07115"],"isi":["001465985500001"]},"author":[{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","last_name":"Roos","first_name":"Barbara","orcid":"0000-0002-9071-5880"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"isi":1,"intvolume":"        13","volume":13,"date_published":"2025-04-14T00:00:00Z","article_processing_charge":"Yes","ddc":["510"],"publisher":"Cambridge University Press","project":[{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"article_number":"e71","year":"2025","OA_type":"gold","title":"Enhanced superconductivity at a corner for the linear BCS equation","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","article_type":"original","oa":1,"has_accepted_license":"1","publication_identifier":{"eissn":["2050-5094"]},"publication":"Forum of Mathematics, Sigma","date_created":"2025-04-27T22:02:14Z","abstract":[{"text":"We consider the critical temperature for superconductivity, defined via the linear BCS equation. We prove that at weak coupling the critical temperature for a sample confined to a quadrant in two dimensions is strictly larger than the one for a half-space, which in turn is strictly larger than the one for  R^2. Furthermore, we prove that the relative difference of the critical temperatures vanishes in the weak coupling limit.","lang":"eng"}],"date_updated":"2025-09-30T12:20:22Z","DOAJ_listed":"1","type":"journal_article","file_date_updated":"2025-05-05T09:41:42Z","PlanS_conform":"1","doi":"10.1017/fms.2024.145","day":"14","publication_status":"published","department":[{"_id":"RoSe"}],"corr_author":"1","month":"04","oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","arxiv":1,"file":[{"file_name":"2025_ForumMathSigma_Roos.pdf","file_id":"19651","date_created":"2025-05-05T09:41:42Z","file_size":631645,"creator":"dernst","date_updated":"2025-05-05T09:41:42Z","success":1,"access_level":"open_access","relation":"main_file","checksum":"b0919b3a14f2cb39f8df0e3f41b8d6f1","content_type":"application/pdf"}],"citation":{"apa":"Roos, B., &#38; Seiringer, R. (2025). Enhanced superconductivity at a corner for the linear BCS equation. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.145\">https://doi.org/10.1017/fms.2024.145</a>","ama":"Roos B, Seiringer R. Enhanced superconductivity at a corner for the linear BCS equation. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href=\"https://doi.org/10.1017/fms.2024.145\">10.1017/fms.2024.145</a>","ieee":"B. Roos and R. Seiringer, “Enhanced superconductivity at a corner for the linear BCS equation,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025.","ista":"Roos B, Seiringer R. 2025. Enhanced superconductivity at a corner for the linear BCS equation. Forum of Mathematics, Sigma. 13, e71.","chicago":"Roos, Barbara, and Robert Seiringer. “Enhanced Superconductivity at a Corner for the Linear BCS Equation.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/fms.2024.145\">https://doi.org/10.1017/fms.2024.145</a>.","short":"B. Roos, R. Seiringer, Forum of Mathematics, Sigma 13 (2025).","mla":"Roos, Barbara, and Robert Seiringer. “Enhanced Superconductivity at a Corner for the Linear BCS Equation.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e71, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/fms.2024.145\">10.1017/fms.2024.145</a>."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"status":"public","scopus_import":"1"},{"external_id":{"pmid":["39926012"],"isi":["001261197700002"]},"_id":"17240","isi":1,"author":[{"full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard"}],"intvolume":"        26","volume":26,"date_published":"2025-01-01T00:00:00Z","pmid":1,"article_processing_charge":"Yes (via OA deal)","page":"203-243","project":[{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publisher":"Springer Nature","ddc":["510"],"year":"2025","article_type":"original","OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion","OA_type":"hybrid","oa":1,"has_accepted_license":"1","abstract":[{"lang":"eng","text":"We prove an upper bound on the energy density of the dilute spin-\\(\\frac {1}{2}\\) Fermi gas capturing the leading correction to the kinetic energy\\(8\\pi a\\rho _\\uparrow\\rho _\\downarrow\\) with an error of size smaller than\\(a\\rho^{2}(a^ 3\\rho)^{1/3-\\varepsilon}\\) for any\\(\\varepsilon> 0\\), where a denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin et al. (Nucl Phys A 176(2):237–260, 1971. https://doi.org/10.1016/0375-9474(71)90267-3)."}],"publication":"Annales Henri Poincare","date_created":"2024-07-14T22:01:12Z","publication_identifier":{"issn":["1424-0637"]},"file_date_updated":"2025-08-05T11:42:27Z","PlanS_conform":"1","type":"journal_article","date_updated":"2026-04-07T13:01:40Z","related_material":{"record":[{"id":"18135","relation":"dissertation_contains","status":"public"}]},"month":"01","corr_author":"1","department":[{"_id":"RoSe"}],"publication_status":"published","doi":"10.1007/s00023-024-01450-1","day":"01","quality_controlled":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ama":"Lauritsen AB. Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion. <i>Annales Henri Poincare</i>. 2025;26:203-243. doi:<a href=\"https://doi.org/10.1007/s00023-024-01450-1\">10.1007/s00023-024-01450-1</a>","apa":"Lauritsen, A. B. (2025). Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-024-01450-1\">https://doi.org/10.1007/s00023-024-01450-1</a>","ieee":"A. B. Lauritsen, “Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion,” <i>Annales Henri Poincare</i>, vol. 26. Springer Nature, pp. 203–243, 2025.","ista":"Lauritsen AB. 2025. Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion. Annales Henri Poincare. 26, 203–243.","mla":"Lauritsen, Asbjørn Bækgaard. “Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion.” <i>Annales Henri Poincare</i>, vol. 26, Springer Nature, 2025, pp. 203–43, doi:<a href=\"https://doi.org/10.1007/s00023-024-01450-1\">10.1007/s00023-024-01450-1</a>.","chicago":"Lauritsen, Asbjørn Bækgaard. “Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion.” <i>Annales Henri Poincare</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00023-024-01450-1\">https://doi.org/10.1007/s00023-024-01450-1</a>.","short":"A.B. Lauritsen, Annales Henri Poincare 26 (2025) 203–243."},"file":[{"relation":"main_file","checksum":"01b6572f55f721e97498522c85072ed2","content_type":"application/pdf","success":1,"access_level":"open_access","file_size":797241,"creator":"dernst","date_updated":"2025-08-05T11:42:27Z","file_name":"2025_AnnalesHenriPoincare_Lauritsen.pdf","file_id":"20125","date_created":"2025-08-05T11:42:27Z"}],"scopus_import":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\nWe thank Alessandro Giuliani and Robert Seiringer for helpful discussions and Robert Seiringer for his comments on the manuscript. Financial support by the Austrian Science Fund (FWF) through Grant https://doi.org/10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged."},{"scopus_import":"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.","file":[{"date_created":"2025-01-09T07:56:28Z","file_id":"18786","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","date_updated":"2025-01-09T07:56:28Z","creator":"dernst","file_size":503910,"access_level":"open_access","success":1,"content_type":"application/pdf","checksum":"2b053a4223b4db14b90520999ec56054","relation":"main_file"}],"citation":{"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>.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","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.","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.","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>"},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","arxiv":1,"doi":"10.1142/s0129055x2360005x","day":"01","ec_funded":1,"publication_status":"published","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"corr_author":"1","month":"10","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"},{"id":"18135","relation":"dissertation_contains","status":"public"}]},"date_updated":"2026-04-07T13:01:40Z","type":"journal_article","file_date_updated":"2025-01-09T07:56:28Z","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"publication":"Reviews in Mathematical Physics","date_created":"2023-11-15T23:48:14Z","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":1,"has_accepted_license":"1","OA_type":"hybrid","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Universality in low-dimensional BCS theory","OA_place":"publisher","article_type":"original","article_number":"2360005 ","year":"2024","ddc":["510"],"publisher":"World Scientific Publishing","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"article_processing_charge":"Yes (in subscription journal)","date_published":"2024-10-01T00:00:00Z","volume":36,"intvolume":"        36","isi":1,"author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"},{"first_name":"Barbara","orcid":"0000-0002-9071-5880","last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara"}],"_id":"14542","external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"issue":"9"},{"article_number":"110320","year":"2024","publisher":"Elsevier","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","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"}],"ddc":["510"],"article_processing_charge":"Yes (via OA deal)","date_published":"2024-04-01T00:00:00Z","volume":286,"intvolume":"       286","isi":1,"author":[{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["2301.04894"],"isi":["001170294000001"]},"_id":"14931","issue":"7","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.","scopus_import":"1","status":"public","citation":{"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>.","short":"A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024).","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.","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.","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>","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>"},"file":[{"file_name":"2024_JourFunctAnalysis_Lauritsen.pdf","date_created":"2024-07-22T11:11:56Z","file_id":"17305","creator":"dernst","file_size":1381063,"date_updated":"2024-07-22T11:11:56Z","access_level":"open_access","success":1,"checksum":"ee203cf2dc4420ad90d3c9970d246a78","relation":"main_file","content_type":"application/pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"arxiv":1,"language":[{"iso":"eng"}],"oa_version":"Published Version","quality_controlled":"1","corr_author":"1","month":"04","related_material":{"record":[{"relation":"dissertation_contains","id":"18135","status":"public"}]},"doi":"10.1016/j.jfa.2024.110320","day":"01","ec_funded":1,"department":[{"_id":"RoSe"}],"publication_status":"published","file_date_updated":"2024-07-22T11:11:56Z","date_updated":"2026-04-16T08:17:56Z","type":"journal_article","abstract":[{"lang":"eng","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]."}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication":"Journal of Functional Analysis","date_created":"2024-02-04T23:00:53Z","oa":1,"has_accepted_license":"1","article_type":"original","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","title":"Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion"},{"_id":"18107","external_id":{"arxiv":["2407.05990"],"isi":["001307817400001"]},"author":[{"last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"isi":1,"intvolume":"        12","volume":12,"date_published":"2024-09-09T00:00:00Z","article_processing_charge":"Yes","publisher":"Cambridge University Press","project":[{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"ddc":["510"],"article_number":"e78","year":"2024","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Pressure of a dilute spin-polarized Fermi gas: Lower bound","has_accepted_license":"1","oa":1,"abstract":[{"text":"We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions  d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order  adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and  ρ  is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).","lang":"eng"}],"publication_identifier":{"issn":["2050-5094"]},"publication":"Forum of Mathematics, Sigma","date_created":"2024-09-20T12:25:25Z","file_date_updated":"2024-09-23T09:56:17Z","date_updated":"2026-04-07T13:01:40Z","type":"journal_article","corr_author":"1","month":"09","related_material":{"record":[{"relation":"dissertation_contains","id":"18135","status":"public"}]},"doi":"10.1017/fms.2024.56","day":"09","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publication_status":"published","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","status":"public","citation":{"ista":"Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.","short":"A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024).","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 12, e78, Cambridge University Press, 2024, doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>.","chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>.","ama":"Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. 2024;12. doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>","ieee":"A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 12. Cambridge University Press, 2024."},"file":[{"file_name":"2024_ForumMath_Lauritsen.pdf","file_id":"18126","date_created":"2024-09-23T09:56:17Z","creator":"dernst","file_size":599886,"date_updated":"2024-09-23T09:56:17Z","access_level":"open_access","success":1,"checksum":"330b881240013213a8e08538fec13d29","relation":"main_file","content_type":"application/pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","acknowledgement":"Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged."},{"file_date_updated":"2024-09-26T13:12:55Z","type":"dissertation","date_updated":"2026-04-16T08:17:55Z","abstract":[{"text":"This thesis consists of two separate parts. In the first part we consider a dilute Fermi gas interacting through a repulsive interaction in dimensions $d=1,2,3$. Our focus is mostly on the physically most relevant dimension $d=3$ \r\nand the setting of a spin-polarized (equivalently spinless) gas, where the Pauli exclusion principle plays a key role. We show that, at zero temperature, the ground state energy density of the interacting spin-polarized gas differs (to leading order) from that of the free (i.e. non-interacting) gas by a term of order $a_p^d\\rho^{2+2/d}$  with $a_p$ the $p$-wave scattering length of the repulsive interaction and $\\rho$ the density. Further, we extend this to positive temperature and show that the pressure of an interacting spin-polarized gas differs from that of the free gas by a now temperature dependent term, again of order $a_p^d\\rho^{2+2/d}$. Lastly, we consider the setting of a spin-$\\frac{1}{2}$ Fermi gas in $d=3$ dimensions and show that here, as an upper bound, the ground state energy density differs from that of the free system by a term of order $a_s \\rho^2$ with an error smaller than $a_s \\rho^2 (a_s\\rho^{1/3})^{1-\\eps}$ for any $\\eps > 0$, where $a_s$ is the $s$-wave scattering length of the repulsive interaction. \r\n\r\nThese asymptotic formulas complement the similar formulas in the literature for the dilute Bose and spin-$\\frac{1}{2}$ Fermi gas, where the ground state energies or pressures differ from that of the corresponding free systems by a term of order $a_s \\rho^2$ in dimension $d=3$. In the spin-polarized setting, the corrections, of order $a_p^3\\rho^{8/3}$ in dimension $d=3$, are thus much smaller and requires a more delicate analysis.\r\n\r\nIn the second part of the thesis we consider the Bardeen--Cooper--Schrieffer (BCS) theory of superconductivity and in particular its associated critical temperature and energy gap. We prove that the ratio of the zero-temperature energy gap and critical temperature $\\Xi(T=0)/T_c$ approaches a universal constant $\\pi e^{-\\gamma}\\approx 1.76$ in both the limit of high density in dimension $d=3$ and in the limit of weak coupling in dimensions $d=1,2$. This complements the proofs in the literature of this universal behaviour in the limit of weak coupling or low density in dimension $d=3$. Secondly, we prove that the ratio of the energy gap at positive temperature and critical temperature $\\Xi(T)/T_c$ approaches a universal function of the relative temperature $T/T_c$ in the limit of weak coupling in dimensions $d=1,2,3$.","lang":"eng"}],"supervisor":[{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"date_created":"2024-09-24T10:56:25Z","publication_identifier":{"isbn":["978-3-99078-042-8"],"issn":["2663-337X"]},"has_accepted_license":"1","oa":1,"OA_place":"publisher","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","title":"Energies of dilute Fermi gases and universalities in BCS theory","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"date_updated":"2024-09-26T13:11:24Z","creator":"alaurits","file_size":3648831,"file_id":"18147","date_created":"2024-09-26T13:11:24Z","file_name":"Lauritsen-thesis-final.pdf","content_type":"application/pdf","checksum":"c7bc3b31e430d57c65393051ca439575","relation":"main_file","access_level":"open_access","success":1},{"access_level":"closed","content_type":"application/x-zip-compressed","relation":"source_file","checksum":"39f6b1b7f83e25a3bf9f933f1ea0bc06","file_id":"18148","date_created":"2024-09-26T13:12:55Z","file_name":"Lauritsen-thesis-source.zip","date_updated":"2024-09-26T13:12:55Z","file_size":1625888,"creator":"alaurits"}],"citation":{"ieee":"A. B. Lauritsen, “Energies of dilute Fermi gases and universalities in BCS theory,” Institute of Science and Technology Austria, 2024.","ama":"Lauritsen AB. Energies of dilute Fermi gases and universalities in BCS theory. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18135\">10.15479/at:ista:18135</a>","apa":"Lauritsen, A. B. (2024). <i>Energies of dilute Fermi gases and universalities in BCS theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18135\">https://doi.org/10.15479/at:ista:18135</a>","mla":"Lauritsen, Asbjørn Bækgaard. <i>Energies of Dilute Fermi Gases and Universalities in BCS Theory</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18135\">10.15479/at:ista:18135</a>.","chicago":"Lauritsen, Asbjørn Bækgaard. “Energies of Dilute Fermi Gases and Universalities in BCS Theory.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18135\">https://doi.org/10.15479/at:ista:18135</a>.","short":"A.B. Lauritsen, Energies of Dilute Fermi Gases and Universalities in BCS Theory, Institute of Science and Technology Austria, 2024.","ista":"Lauritsen AB. 2024. Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria."},"oa_version":"Published Version","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"11732","status":"public"},{"status":"public","id":"14542","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"18107","status":"public"},{"id":"17240","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"14931"}]},"corr_author":"1","month":"09","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"doi":"10.15479/at:ista:18135","ec_funded":1,"day":"23","author":[{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"}],"alternative_title":["ISTA Thesis"],"_id":"18135","year":"2024","degree_awarded":"PhD","project":[{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"},{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"publisher":"Institute of Science and Technology Austria","ddc":["515","539"],"article_processing_charge":"No","page":"353","date_published":"2024-09-23T00:00:00Z"},{"oa":1,"has_accepted_license":"1","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","title":"Boundary superconductivity in BCS theory","OA_place":"publisher","date_updated":"2026-04-07T13:27:39Z","type":"dissertation","file_date_updated":"2023-10-06T11:38:01Z","publication_identifier":{"issn":["2663-337X"]},"supervisor":[{"orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"date_created":"2023-09-28T14:23:04Z","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"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.15479/at:ista:14374","ec_funded":1,"day":"30","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"month":"09","corr_author":"1","related_material":{"record":[{"relation":"part_of_dissertation","id":"10850","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"13207"}]},"citation":{"ieee":"B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023.","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>","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>","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>.","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>.","short":"B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023.","ista":"Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science and Technology Austria."},"file":[{"creator":"broos","file_size":2365702,"date_updated":"2023-10-06T11:35:56Z","file_name":"phd-thesis-draft_pdfa_acrobat.pdf","file_id":"14398","date_created":"2023-10-06T11:35:56Z","checksum":"ef039ffc3de2cb8dee5b14110938e9b6","relation":"main_file","content_type":"application/pdf","access_level":"open_access"},{"creator":"broos","file_size":4691734,"date_updated":"2023-10-06T11:38:01Z","file_name":"Version5.zip","file_id":"14399","date_created":"2023-10-06T11:38:01Z","checksum":"81dcac33daeefaf0111db52f41bb1fd0","relation":"source_file","content_type":"application/x-zip-compressed","access_level":"closed"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"status":"public","author":[{"full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","last_name":"Roos","orcid":"0000-0002-9071-5880","first_name":"Barbara"}],"_id":"14374","alternative_title":["ISTA Thesis"],"page":"206","article_processing_charge":"No","date_published":"2023-09-30T00:00:00Z","degree_awarded":"PhD","year":"2023","ddc":["515","539"],"publisher":"Institute of Science and Technology Austria","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}]}]