{"isi":1,"article_processing_charge":"No","day":"18","has_accepted_license":"1","doi":"10.4171/JST/439","file":[{"date_updated":"2023-07-11T08:19:15Z","file_size":304619,"date_created":"2023-07-11T08:19:15Z","creator":"alisjak","relation":"main_file","access_level":"open_access","checksum":"5501da33be010b5c81440438287584d5","file_id":"13208","file_name":"2023_EMS_Hainzl.pdf","content_type":"application/pdf","success":1}],"file_date_updated":"2023-07-11T08:19:15Z","publisher":"EMS Press","oa":1,"date_created":"2023-07-10T16:35:45Z","language":[{"iso":"eng"}],"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"}],"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.","related_material":{"record":[{"id":"14374","relation":"dissertation_contains","status":"public"}]},"intvolume":"        12","publication_identifier":{"issn":["1664-039X"],"eissn":["1664-0403"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","author":[{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","publication_status":"published","date_published":"2023-05-18T00:00:00Z","date_updated":"2023-10-27T10:37:29Z","volume":12,"project":[{"call_identifier":"H2020","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"ddc":["530"],"article_type":"original","year":"2023","ec_funded":1,"status":"public","oa_version":"Published Version","publication":"Journal of Spectral Theory","external_id":{"arxiv":["2201.08090"],"isi":["000997933500008"]},"issue":"4","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Boundary superconductivity in the BCS model","month":"05","_id":"13207","citation":{"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>","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>.","ista":"Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 12(4), 1507–1540.","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.","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>","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>.","short":"C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540."},"page":"1507–1540"}