[{"article_type":"original","month":"01","oa":1,"has_accepted_license":"1","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha"},{"full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard"}],"citation":{"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>.","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>.","ista":"Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352.","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.","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>","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.","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>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","OA_type":"gold","day":"09","ec_funded":1,"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"file_date_updated":"2025-04-11T09:13:31Z","page":"305–352","abstract":[{"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 .","lang":"eng"}],"intvolume":"        15","OA_place":"publisher","external_id":{"arxiv":["2312.11310"],"isi":["001438931600009"]},"ddc":["500"],"_id":"19548","publisher":"EMS Press","date_published":"2025-01-09T00:00:00Z","quality_controlled":"1","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"},{"_id":"RoSe"}],"date_created":"2025-04-11T09:19:28Z","tmp":{"image":"/images/cc_by.png","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"},"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","publication_identifier":{"eissn":["1664-0403"]},"doi":"10.4171/JST/540","article_processing_charge":"No","title":"Universal behavior of the BCS energy gap","corr_author":"1","type":"journal_article","publication":"Journal of Spectral Theory","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"file":[{"access_level":"open_access","checksum":"f49e06e8dba819f7ad52a202e287ebca","content_type":"application/pdf","success":1,"file_id":"19549","creator":"cchlebak","date_updated":"2025-04-11T09:13:31Z","file_name":"Henheik_JSpectralTheory_2025.pdf","file_size":779158,"relation":"main_file","date_created":"2025-04-11T09:13:31Z"}],"issue":"1","scopus_import":"1","oa_version":"Published Version","DOAJ_listed":"1","year":"2025","arxiv":1,"isi":1,"volume":15,"status":"public","date_updated":"2026-04-07T12:37:11Z"}]