[{"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Edwin","last_name":"Langmann","full_name":"Langmann, Edwin"},{"orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"}],"language":[{"iso":"eng"}],"day":"29","status":"public","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"OA_type":"hybrid","abstract":[{"text":"We introduce a multi-band BCS free energy functional and prove that for a multi-band superconductor the effect of inter-band coupling can only increase the critical temperature, irrespective of its attractive or repulsive nature and its strength. Further, for weak coupling and weaker inter-band coupling, we prove that the dependence of the increase in critical temperature on the inter-band coupling is (1) linear, if there are two or more equally strongly superconducting bands, or (2) quadratic, if there is only one dominating band.","lang":"eng"}],"external_id":{"arxiv":["2409.17297"]},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"_id":"22290","supplementarymaterial":"not applicable","scopus_import":"1","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"acknowledgement":"We would like to thank J. Lenells and R. Seiringer for their interest and helpful discussions, E. Babaev and Y. Yerin for useful comments about the literature, and the anonymous referee for their comments. J.H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331 and the ERC Consollidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education, Research and Innovation). E.L. gratefully acknowledges support from the Swedish Research Council, Grant No. 2023-04726. A.B.L. gratefully acknowledges partial financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) and by the French State support managed by ANR under the France 2030 program through the MaQuI CNRS Risky and High-Impact Research programme (RI)^2 (grant agreement ANR-24-RRII-0001). Open access funding provided by Royal Institute of Technology.","citation":{"short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026).","apa":"Henheik, S. J., Langmann, E., & Lauritsen, A. B. (2026). Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-026-01706-y","mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” Annales Henri Poincaré, Springer Nature, 2026, doi:10.1007/s00023-026-01706-y.","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” Annales Henri Poincaré. Springer Nature, 2026.","ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré. 2026. doi:10.1007/s00023-026-01706-y","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” Annales Henri Poincaré. Springer Nature, 2026. https://doi.org/10.1007/s00023-026-01706-y.","ista":"Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré."},"das_tickbox":"1","researchdata_availability":"not applicable","publisher":"Springer Nature","ddc":["500"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"main_file_link":[{"url":"https://doi.org/10.1007/s00023-026-01706-y","open_access":"1"}],"quality_controlled":"1","article_type":"original","oa_version":"Published Version","has_accepted_license":"1","OA_place":"publisher","date_published":"2026-06-29T00:00:00Z","doi":"10.1007/s00023-026-01706-y","title":"Multi-band superconductors have enhanced critical temperatures","dataavailabilitystatement":"Data sharing is not applicable to this article as no new data were created or analyzed in this study.","article_processing_charge":"Yes (via OA deal)","month":"06","oa":1,"related_material":{"record":[{"status":"public","id":"19550","relation":"earlier_version"}]},"date_created":"2026-07-13T09:42:22Z","fulldoi":"https://doi.org/10.1007/s00023-026-01706-y","publication":"Annales Henri Poincaré","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication_status":"epub_ahead","PlanS_conform":"1","date_updated":"2026-07-13T11:34:08Z","year":"2026","type":"journal_article"},{"volume":116,"intvolume":" 116","date_updated":"2026-07-23T06:42:28Z","PlanS_conform":"1","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"publication":"Letters in Mathematical Physics","publication_status":"published","fulldoi":"https://doi.org/10.1007/s11005-025-02037-5","file":[{"checksum":"f2021f8f6d38491948b94a7765a64d0b","file_size":602526,"file_id":"22390","access_level":"open_access","date_created":"2026-07-23T06:42:01Z","file_name":"2026_LettersMathPhysics_Erdoes.pdf","date_updated":"2026-07-23T06:42:01Z","success":1,"creator":"dernst","content_type":"application/pdf","relation":"main_file"}],"date_created":"2026-01-04T23:01:33Z","type":"journal_article","year":"2026","corr_author":"1","has_accepted_license":"1","oa_version":"Published Version","article_type":"original","pmid":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","ddc":["510"],"doi":"10.1007/s11005-025-02037-5","date_published":"2026-02-01T00:00:00Z","OA_place":"publisher","article_processing_charge":"Yes (via OA deal)","dataavailabilitystatement":"The Matlab code used to generate the datasets of the provided examples is available from the corresponding author on request.","title":"Normal typicality and dynamical typicality for a random block-band matrix model","oa":1,"month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"5","ec_funded":1,"das_tickbox":"1","citation":{"ista":"Erdös L, Henheik SJ, Vogel C. 2026. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 116, 5.","chicago":"Erdös, László, Sven Joscha Henheik, and Cornelia Vogel. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics. Springer Nature, 2026. https://doi.org/10.1007/s11005-025-02037-5.","ieee":"L. Erdös, S. J. Henheik, and C. Vogel, “Normal typicality and dynamical typicality for a random block-band matrix model,” Letters in Mathematical Physics, vol. 116. Springer Nature, 2026.","mla":"Erdös, László, et al. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics, vol. 116, 5, Springer Nature, 2026, doi:10.1007/s11005-025-02037-5.","ama":"Erdös L, Henheik SJ, Vogel C. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 2026;116. doi:10.1007/s11005-025-02037-5","short":"L. Erdös, S.J. Henheik, C. Vogel, Letters in Mathematical Physics 116 (2026).","apa":"Erdös, L., Henheik, S. J., & Vogel, C. (2026). Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-02037-5"},"acknowledgement":"L.E. and J.H. are supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. Moreover, J.H. acknowledges (partial) financial support by the ERC Consolidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education, Research and Innovation). C.V. was (partially) supported by the German Academic Scholarship Foundation and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – TRR 352 – Project-ID 470903074. Moreover, C.V. acknowledges (partial) financial support by the ERC Starting Grant “FermiMath\" No. 101040991 and the ERC Consolidator Grant “RAMBAS” No. 10104424, funded by the European Union. Open access funding provided by Institute of Science and Technology (IST Austria).","_id":"20925","supplementarymaterial":"yes","scopus_import":"1","department":[{"_id":"LaEr"}],"researchdata_availability":"upon request","publisher":"Springer Nature","file_date_updated":"2026-07-23T06:42:01Z","day":"01","language":[{"iso":"eng"}],"mathsc":["60B20","82C10"],"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"last_name":"Vogel","full_name":"Vogel, Cornelia","id":"1cd0554a-ea28-11f0-9f40-ff76440883cd","first_name":"Cornelia"}],"status":"public","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"external_id":{"pmid":["41459414"]},"abstract":[{"lang":"eng","text":"We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices (Erdős and Riabov in Commun Math Phys 405(12): 282, 2024) and an intricate analysis of the deterministic approximation."}],"OA_type":"hybrid"},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"253","issue":"10","publisher":"Springer Nature","scopus_import":"1","_id":"20322","department":[{"_id":"LaEr"}],"citation":{"ista":"Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253.","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s00220-025-05417-z.","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics, vol. 406, no. 10, 253, Springer Nature, 2025, doi:10.1007/s00220-025-05417-z.","ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” Communications in Mathematical Physics, vol. 406, no. 10. Springer Nature, 2025.","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 2025;406(10). doi:10.1007/s00220-025-05417-z","short":"L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025).","apa":"Erdös, L., Henheik, S. J., & Riabov, V. (2025). Cusp universality for correlated random matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-025-05417-z"},"acknowledgement":"We thank Giorgio Cipolloni for many productive discussions and the anonymous referees for several useful suggestions and spotting some typos. Open access funding provided by Institute of Science and Technology (IST Austria).","status":"public","language":[{"iso":"eng"}],"author":[{"last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr"}],"file_date_updated":"2025-09-10T07:48:21Z","day":"01","arxiv":1,"abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the Zigzag strategy, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.","lang":"eng"}],"external_id":{"arxiv":["2410.06813"],"isi":["001565019000005"]},"OA_type":"hybrid","intvolume":" 406","isi":1,"volume":406,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"19547"},{"status":"public","id":"20575","relation":"dissertation_contains"}]},"type":"journal_article","year":"2025","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication":"Communications in Mathematical Physics","publication_status":"published","fulldoi":"https://doi.org/10.1007/s00220-025-05417-z","file":[{"relation":"main_file","content_type":"application/pdf","creator":"dernst","success":1,"date_updated":"2025-09-10T07:48:21Z","file_name":"2025_CommMathPhysics_Erdoes.pdf","date_created":"2025-09-10T07:48:21Z","access_level":"open_access","file_id":"20336","file_size":1465827,"checksum":"abd32af7b8ca6dc5b9080823a433986b"}],"date_created":"2025-09-10T05:38:17Z","date_updated":"2026-04-07T12:32:19Z","PlanS_conform":"1","date_published":"2025-09-01T00:00:00Z","OA_place":"publisher","doi":"10.1007/s00220-025-05417-z","oa_version":"Published Version","article_type":"original","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","corr_author":"1","has_accepted_license":"1","month":"09","oa":1,"title":"Cusp universality for correlated random matrices","article_processing_charge":"Yes (via OA deal)"},{"status":"public","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"day":"20","author":[{"last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang"},{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"orcid":"0000-0003-1491-4623","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev"}],"language":[{"iso":"eng"}],"arxiv":1,"OA_type":"hybrid","abstract":[{"text":"We consider the Wigner minor process, i.e. the eigenvalues of an N\\times N Wigner matrix H^{(N)} together with the eigenvalues of all its n\\times n minors, H^{(n)}, n\\le N. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.","lang":"eng"}],"external_id":{"arxiv":["2503.06549"],"isi":["001574640900001"]},"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121 and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","citation":{"chicago":"Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” Probability Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01422-4.","ista":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields.","apa":"Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01422-4","short":"Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025).","mla":"Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” Probability Theory and Related Fields, Springer Nature, 2025, doi:10.1007/s00440-025-01422-4.","ieee":"Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” Probability Theory and Related Fields. Springer Nature, 2025.","ama":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. 2025. doi:10.1007/s00440-025-01422-4"},"_id":"20478","scopus_import":"1","department":[{"_id":"LaEr"}],"doi":"10.1007/s00440-025-01422-4","OA_place":"publisher","date_published":"2025-09-20T00:00:00Z","corr_author":"1","ddc":["500"],"main_file_link":[{"url":"https://doi.org/10.1007/s00440-025-01422-4","open_access":"1"}],"quality_controlled":"1","oa_version":"Published Version","article_type":"original","oa":1,"month":"09","article_processing_charge":"Yes (via OA deal)","title":"Decorrelation transition in the Wigner minor process","isi":1,"year":"2025","type":"journal_article","PlanS_conform":"1","date_updated":"2026-06-18T18:23:40Z","fulldoi":"https://doi.org/10.1007/s00440-025-01422-4","date_created":"2025-10-16T13:10:26Z","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"publication_status":"epub_ahead","publication":"Probability Theory and Related Fields"},{"year":"2025","type":"preprint","fulldoi":"https://doi.org/10.48550/ARXIV.2511.10398","date_created":"2026-07-14T12:51:50Z","publication_status":"draft","publication":"arXiv","date_updated":"2026-07-20T14:58:23Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"22255"}]},"month":"11","oa":1,"keyword":["Differential Geometry (math.DG)","Mathematical Physics (math-ph)","Dynamical Systems (math.DS)","Spectral Theory (math.SP)","FOS: Mathematics","FOS: Mathematics","FOS: Physical sciences","FOS: Physical sciences","58J42","37J35","37J35","35P20","58J40","58J50","37D40"],"title":"Spectral rigidity of Liouville tori","article_processing_charge":"No","OA_place":"repository","date_published":"2025-11-13T00:00:00Z","doi":"10.48550/ARXIV.2511.10398","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2511.10398","open_access":"1"}],"oa_version":"Preprint","corr_author":"1","_id":"22340","department":[{"_id":"VaKa"},{"_id":"LaEr"}],"citation":{"ista":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv, 10.48550/ARXIV.2511.10398.","chicago":"Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral Rigidity of Liouville Tori.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2511.10398.","ama":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv. doi:10.48550/ARXIV.2511.10398","ieee":"S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville tori,” arXiv. .","mla":"Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” ArXiv, doi:10.48550/ARXIV.2511.10398.","short":"S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).","apa":"Henheik, S. J., Kaloshin, V., Li, Y., & Vig, A. (n.d.). Spectral rigidity of Liouville tori. arXiv. https://doi.org/10.48550/ARXIV.2511.10398"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","arxiv":1,"OA_type":"green","external_id":{"arxiv":["2511.10398"]},"abstract":[{"text":"We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary.","lang":"eng"}],"status":"public","author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"Yunzhe","id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31","full_name":"Li, Yunzhe","last_name":"Li"},{"first_name":"Amir","last_name":"Vig","full_name":"Vig, Amir","id":"49d58dd5-45f5-11ec-9f86-8ce1276989b9"}],"language":[{"iso":"eng"}],"day":"13"},{"isi":1,"volume":45,"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"intvolume":" 45","fulldoi":"https://doi.org/10.1017/etds.2024.48","date_created":"2024-09-22T22:01:43Z","file":[{"file_id":"18828","file_size":659100,"checksum":"650fe115d998fe0ac3a8d0c7519447c8","access_level":"open_access","date_created":"2025-01-13T08:51:40Z","success":1,"date_updated":"2025-01-13T08:51:40Z","file_name":"2025_ErgodicTheory_Henheik.pdf","content_type":"application/pdf","creator":"dernst","relation":"main_file"}],"publication_identifier":{"issn":["0143-3857"],"eissn":["1469-4417"]},"publication_status":"published","publication":"Ergodic Theory and Dynamical Systems","date_updated":"2026-07-29T13:18:16Z","year":"2025","type":"journal_article","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"quality_controlled":"1","article_type":"original","oa_version":"Published Version","page":"467-503","has_accepted_license":"1","corr_author":"1","OA_place":"publisher","date_published":"2025-02-01T00:00:00Z","doi":"10.1017/etds.2024.48","title":"Deformational rigidity of integrable metrics on the torus","article_processing_charge":"Yes (via OA deal)","month":"02","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","ec_funded":1,"scopus_import":"1","_id":"18112","department":[{"_id":"LaEr"}],"acknowledgement":"I am very grateful to Vadim Kaloshin for suggesting the topic, his guidance during this project, and many helpful comments on an earlier version of the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr Riabov for interesting discussions. Partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received funding from the European Research Council (ERC) ERC Grant No. 885707.","citation":{"ama":"Henheik SJ. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 2025;45(2):467-503. doi:10.1017/etds.2024.48","ieee":"S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,” Ergodic Theory and Dynamical Systems, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025.","mla":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:10.1017/etds.2024.48.","apa":"Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2024.48","short":"S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.","ista":"Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503.","chicago":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2025. https://doi.org/10.1017/etds.2024.48."},"publisher":"Cambridge University Press","author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"}],"language":[{"iso":"eng"}],"day":"01","file_date_updated":"2025-01-13T08:51:40Z","status":"public","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"},{"grant_number":"885707","call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"OA_type":"hybrid","external_id":{"isi":["001308182000001"]},"abstract":[{"lang":"eng","text":"It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus."}]},{"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"status":"public","language":[{"iso":"eng"}],"author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","last_name":"Kolupaiev","orcid":"0000-0003-1491-4623","first_name":"Oleksii"}],"file_date_updated":"2025-02-05T07:01:40Z","day":"30","arxiv":1,"abstract":[{"lang":"eng","text":"We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2."}],"external_id":{"arxiv":["2410.08108"],"pmid":["39896265"],"isi":["001409618800002"]},"OA_type":"hybrid","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"14","publisher":"Springer Nature","_id":"19001","department":[{"_id":"LaEr"}],"scopus_import":"1","citation":{"chicago":"Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s11005-025-01904-5.","ista":"Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14.","short":"L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025).","apa":"Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-01904-5","ama":"Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 2025;115. doi:10.1007/s11005-025-01904-5","mla":"Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics, vol. 115, 14, Springer Nature, 2025, doi:10.1007/s11005-025-01904-5.","ieee":"L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” Letters in Mathematical Physics, vol. 115. Springer Nature, 2025."},"acknowledgement":"We thank Giorgio Cipolloni for helpful discussions in a closely related joint project. Open access funding provided by Institute of Science and Technology (IST Austria). All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","date_published":"2025-01-30T00:00:00Z","OA_place":"publisher","doi":"10.1007/s11005-025-01904-5","oa_version":"Published Version","article_type":"original","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"pmid":1,"quality_controlled":"1","corr_author":"1","has_accepted_license":"1","month":"01","oa":1,"title":"Loschmidt echo for deformed Wigner matrices","article_processing_charge":"Yes (via OA deal)","intvolume":" 115","volume":115,"isi":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"type":"journal_article","year":"2025","publication_status":"published","publication":"Letters in Mathematical Physics","publication_identifier":{"issn":["1573-0530"]},"file":[{"content_type":"application/pdf","creator":"dernst","relation":"main_file","checksum":"ee07edf5f85a6f2651926b2f8760af74","file_size":828335,"file_id":"19004","access_level":"open_access","date_created":"2025-02-05T07:01:40Z","file_name":"2025_LettersMathPhysics_Erdoes.pdf","success":1,"date_updated":"2025-02-05T07:01:40Z"}],"fulldoi":"https://doi.org/10.1007/s11005-025-01904-5","date_created":"2025-02-05T06:48:29Z","date_updated":"2026-07-29T13:18:16Z"},{"corr_author":"1","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10718","open_access":"1"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"doi":"10.48550/arXiv.2410.10718","date_published":"2025-01-30T00:00:00Z","OA_place":"repository","article_processing_charge":"No","title":"Eigenvector decorrelation for random matrices","oa":1,"month":"01","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"date_updated":"2026-07-29T13:18:16Z","publication_status":"draft","publication":"arXiv","date_created":"2025-04-11T08:34:49Z","fulldoi":"https://doi.org/10.48550/arXiv.2410.10718","type":"preprint","year":"2025","day":"30","language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"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":"Oleksii","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii"}],"status":"public","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"abstract":[{"text":"We study the sensitivity of the eigenvectors of random matrices, showing that\r\neven small perturbations make the eigenvectors almost orthogonal. More\r\nprecisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show\r\nthat their bulk eigenvectors become asymptotically orthogonal as soon as\r\n$\\mathrm{Tr}(D_1-D_2)^2\\gg 1$, or their respective energies are separated on a\r\nscale much bigger than the local eigenvalue spacing. Furthermore, we show that\r\nquadratic forms of eigenvectors of $W+D_1$, $W+D_2$ with any deterministic\r\nmatrix $A\\in\\mathbf{C}^{N\\times N}$ in a specific subspace of codimension one\r\nare of size $N^{-1/2}$. This proves a generalization of the Eigenstate\r\nThermalization Hypothesis to eigenvectors belonging to two different spectral\r\nfamilies.","lang":"eng"}],"external_id":{"arxiv":["2410.10718"]},"arxiv":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","ec_funded":1,"citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv. doi:10.48550/arXiv.2410.10718","mla":"Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.10718.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” arXiv. .","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (n.d.). Eigenvector decorrelation for random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.10718","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, 10.48550/arXiv.2410.10718.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10718."},"acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"_id":"19546"},{"abstract":[{"text":"This thesis deals with several different models for complex quantum mechanical systems and is structured in three main parts. \r\n\t\r\nIn Part I, we study mean field random matrices as models for quantum Hamiltonians. Our focus lies on proving concentration estimates for resolvents of random matrices, so-called local laws, mostly in the setting of multiple resolvents. These estimates have profound consequences for eigenvector overlaps and thermalization problems. More concretely, we obtain, e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector overlaps, and prethermalization for deformed Wigner matrices.\tIn order to prove our novel multi-resolvent local laws, we develop and devise two main methods, the static Psi-method and the dynamical Zigzag strategy. \r\n\t\r\nIn Part II, we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic theory of superconductivity. We focus on asymptotic formulas for the characteristic critical temperature and energy gap of a superconductor and prove universality of their ratio in various physical regimes. Additionally, we investigate multi-band superconductors and show that inter-band coupling effects can only enhance the critical temperature. \r\n\t\r\nIn Part III, we study quantum lattice systems. On the one hand, we show a strong version of the local-perturbations-perturb-locally (LPPL) principle for the ground state of weakly interacting quantum spin systems with a uniform on-site gap. On the other hand, we introduce a notion of a local gap and rigorously justify response theory and the Kubo formula under the weakened assumption of a local gap. \r\n\t\r\nAdditionally, we discuss two classes of problems which do not fit into the three main parts of the thesis. These are deformational rigidity of Liouville metrics on the torus and relativistic toy models of particle creation via interior-boundary-conditions (IBCs). ","lang":"eng"}],"project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"status":"public","file_date_updated":"2025-04-23T14:11:05Z","day":"10","language":[{"iso":"eng"}],"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"}],"publisher":"Institute of Science and Technology Austria","citation":{"chicago":"Henheik, Sven Joscha. “Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-19540.","ista":"Henheik SJ. 2025. Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria.","short":"S.J. Henheik, Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.","apa":"Henheik, S. J. (2025). Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-19540","ieee":"S. J. Henheik, “Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems,” Institute of Science and Technology Austria, 2025.","mla":"Henheik, Sven Joscha. Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-19540.","ama":"Henheik SJ. 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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","citation":{"apa":"Henheik, S. J., & Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/540","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.","ama":"Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 2025;15(1):305–352. doi:10.4171/JST/540","ieee":"S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,” Journal of Spectral Theory, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:10.4171/JST/540.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory. EMS Press, 2025. https://doi.org/10.4171/JST/540.","ista":"Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352."},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"status":"public","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen"}],"language":[{"iso":"eng"}],"day":"09","file_date_updated":"2025-04-11T09:13:31Z","arxiv":1,"OA_type":"gold","external_id":{"arxiv":["2312.11310"],"isi":["001438931600009"]},"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"}],"DOAJ_listed":"1","intvolume":" 15","isi":1,"volume":15,"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"year":"2025","type":"journal_article","fulldoi":"https://doi.org/10.4171/JST/540","file":[{"date_created":"2025-04-11T09:13:31Z","date_updated":"2025-04-11T09:13:31Z","success":1,"file_name":"Henheik_JSpectralTheory_2025.pdf","file_size":779158,"file_id":"19549","checksum":"f49e06e8dba819f7ad52a202e287ebca","access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"cchlebak"}],"date_created":"2025-04-11T09:19:28Z","publication_status":"published","publication":"Journal of Spectral Theory","publication_identifier":{"eissn":["1664-0403"]},"date_updated":"2026-07-29T13:18:17Z","OA_place":"publisher","date_published":"2025-01-09T00:00:00Z","doi":"10.4171/JST/540","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","ddc":["500"],"article_type":"original","oa_version":"Published Version","page":"305–352","has_accepted_license":"1","corr_author":"1","month":"01","oa":1,"title":"Universal behavior of the BCS energy gap","article_processing_charge":"No"},{"related_material":{"record":[{"relation":"earlier_version","id":"17174","status":"public"},{"id":"20575","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"19540"}]},"volume":26,"isi":1,"intvolume":" 26","date_updated":"2026-07-29T13:18:17Z","fulldoi":"https://doi.org/10.1007/s00023-024-01518-y","file":[{"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_size":977773,"file_id":"19895","checksum":"49e6a934db540206f7eaa0c798553ded","access_level":"open_access","date_created":"2025-06-25T05:38:34Z","date_updated":"2025-06-25T05:38:34Z","success":1,"file_name":"2025_AnnalesHenriPoincare_Erdoes.pdf"}],"date_created":"2025-01-05T23:01:59Z","publication_status":"published","publication":"Annales Henri Poincare","publication_identifier":{"issn":["1424-0637"]},"year":"2025","type":"journal_article","page":"1991-2033","has_accepted_license":"1","corr_author":"1","quality_controlled":"1","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"article_type":"original","oa_version":"Published Version","doi":"10.1007/s00023-024-01518-y","OA_place":"publisher","date_published":"2025-06-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","title":"Prethermalization for deformed Wigner matrices","oa":1,"month":"06","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ec_funded":1,"acknowledgement":"All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nJ.R. was additionally supported by the ERC Advanced Grant “LDRaM” No. 884584.\r\nWe thank Peter Reimann and Lennart Dabelow for helpful comments. Open access funding provided by Institute of Science and Technology (IST Austria).","citation":{"ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 2025;26:1991-2033. doi:10.1007/s00023-024-01518-y","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner matrices,” Annales Henri Poincare, vol. 26. Springer Nature, pp. 1991–2033, 2025.","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:10.1007/s00023-024-01518-y.","apa":"Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (2025). Prethermalization for deformed Wigner matrices. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-024-01518-y","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033.","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 26, 1991–2033.","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare. Springer Nature, 2025. https://doi.org/10.1007/s00023-024-01518-y."},"department":[{"_id":"LaEr"}],"_id":"18764","scopus_import":"1","publisher":"Springer Nature","day":"01","file_date_updated":"2025-06-25T05:38:34Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","first_name":"Jana"},{"full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov","first_name":"Volodymyr"}],"language":[{"iso":"eng"}],"status":"public","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"OA_type":"hybrid","abstract":[{"lang":"eng","text":"We prove that a class of weakly perturbed Hamiltonians of the form H_λ= H_0 + λW, with W being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by H_λ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order λ^{-2}. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix H_λ."}],"external_id":{"isi":["001385326500001"],"arxiv":["2310.06677"]},"arxiv":1},{"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"date_updated":"2026-07-29T13:18:16Z","publication":"arXiv","publication_status":"draft","date_created":"2025-04-11T12:07:25Z","fulldoi":"https://doi.org/10.48550/arXiv.2409.00677","type":"preprint","year":"2025","corr_author":"1","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.00677"}],"doi":"10.48550/arXiv.2409.00677","date_published":"2025-02-28T00:00:00Z","OA_place":"repository","article_processing_charge":"No","title":"How a space-time singularity helps remove the ultraviolet divergence problem","oa":1,"month":"02","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","ec_funded":1,"citation":{"ama":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. doi:10.48550/arXiv.2409.00677","mla":"Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, doi:10.48550/arXiv.2409.00677.","ieee":"S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps remove the ultraviolet divergence problem,” arXiv. .","apa":"Henheik, S. J., Poudyal, B., & Tumulka, R. (n.d.). How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. https://doi.org/10.48550/arXiv.2409.00677","short":"S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.).","ista":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv, 10.48550/arXiv.2409.00677.","chicago":"Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.00677."},"acknowledgement":"JH gratefully acknowledges partial financial support by the ERC Advanced\r\nGrant “RMTBeyond” No. 101020331.","_id":"19552","department":[{"_id":"LaEr"}],"day":"28","language":[{"iso":"eng"}],"author":[{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Bipul","full_name":"Poudyal, Bipul","last_name":"Poudyal"},{"full_name":"Tumulka, Roderich","last_name":"Tumulka","first_name":"Roderich"}],"status":"public","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"abstract":[{"lang":"eng","text":"Particle creation terms in quantum Hamiltonians are usually ultraviolet\r\ndivergent and thus mathematically ill defined. A rather novel way of solving\r\nthis problem is based on imposing so-called interior-boundary conditions on the\r\nwave function. Previous papers showed that this approach works in the\r\nnon-relativistic regime, but particle creation is mostly relevant in the\r\nrelativistic case after all. In flat relativistic space-time (that is,\r\nneglecting gravity), the approach was previously found to work only for certain\r\nsomewhat artificial cases. Here, as a way of taking gravity into account, we\r\nconsider curved space-time, specifically the super-critical\r\nReissner-Nordstr\\\"om space-time, which features a naked timelike singularity.\r\nWe find that the interior-boundary approach works fully in this setting; in\r\nparticular, we prove rigorously the existence of well-defined, self-adjoint\r\nHamiltonians with particle creation at the singularity, based on\r\ninterior-boundary conditions. We also non-rigorously analyze the asymptotic\r\nbehavior of the Bohmian trajectories and construct the corresponding Bohm-Bell\r\nprocess of particle creation, motion, and annihilation. The upshot is that in\r\nquantum physics, a naked space-time singularity need not lead to a breakdown of\r\nphysical laws, but on the contrary allows for boundary conditions governing\r\nwhat comes out of the singularity and thereby removing the ultraviolet\r\ndivergence."}],"external_id":{"arxiv":["2409.00677"]},"arxiv":1},{"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"status":"public","day":"17","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"}],"language":[{"iso":"eng"}],"arxiv":1,"external_id":{"arxiv":["2309.05488"]},"abstract":[{"text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling.","lang":"eng"}],"ec_funded":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","apa":"Cipolloni, G., Erdös, L., & Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. arXiv. https://doi.org/10.48550/arXiv.2309.05488","ama":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, doi:10.48550/arXiv.2309.05488.","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” arXiv. .","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.05488.","ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, 10.48550/arXiv.2309.05488."},"department":[{"_id":"LaEr"}],"_id":"19545","doi":"10.48550/arXiv.2309.05488","OA_place":"repository","date_published":"2024-12-17T00:00:00Z","corr_author":"1","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.05488","open_access":"1"}],"oa_version":"Preprint","oa":1,"month":"12","article_processing_charge":"No","title":"Eigenstate thermalisation at the edge for Wigner matrices","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"year":"2024","type":"preprint","date_updated":"2026-07-29T13:18:16Z","fulldoi":"https://doi.org/10.48550/arXiv.2309.05488","date_created":"2025-04-11T08:19:22Z","publication":"arXiv","publication_status":"draft"},{"year":"2024","type":"preprint","citation":{"ista":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, 10.48550/arXiv.2409.17297.","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.17297.","ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv. doi:10.48550/arXiv.2409.17297","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” arXiv. .","mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” ArXiv, doi:10.48550/arXiv.2409.17297.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","apa":"Henheik, S. J., Langmann, E., & Lauritsen, A. B. (n.d.). Multi-band superconductors have enhanced critical temperatures. arXiv. https://doi.org/10.48550/arXiv.2409.17297"},"date_updated":"2026-07-29T13:18:16Z","fulldoi":"https://doi.org/10.48550/arXiv.2409.17297","date_created":"2025-04-11T11:43:58Z","_id":"19550","publication_status":"draft","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"publication":"arXiv","related_material":{"record":[{"relation":"later_version","id":"22290","status":"public"},{"status":"public","id":"19540","relation":"dissertation_contains"}]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","arxiv":1,"oa":1,"month":"10","article_processing_charge":"No","title":"Multi-band superconductors have enhanced critical temperatures","external_id":{"arxiv":["2409.17297"]},"abstract":[{"text":"We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band superconductor the effect of inter-band coupling can only increase\r\nthe critical temperature, irrespective of its attractive or repulsive nature\r\nand its strength. Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the dependence of the increase in critical temperature on the\r\ninter-band coupling is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands, or (2) quadratic, if there is only one dominating band.","lang":"eng"}],"status":"public","doi":"10.48550/arXiv.2409.17297","OA_place":"repository","date_published":"2024-10-21T00:00:00Z","day":"21","corr_author":"1","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.17297","open_access":"1"}],"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"full_name":"Langmann, Edwin","last_name":"Langmann","first_name":"Edwin"},{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"language":[{"iso":"eng"}],"oa_version":"Preprint"},{"doi":"10.1016/j.jfa.2024.110495","OA_place":"publisher","date_published":"2024-08-15T00:00:00Z","has_accepted_license":"1","corr_author":"1","quality_controlled":"1","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"article_type":"original","oa_version":"Published Version","oa":1,"month":"08","article_processing_charge":"Yes (via OA deal)","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","intvolume":" 287","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"isi":1,"volume":287,"year":"2024","type":"journal_article","date_updated":"2026-07-29T13:18:17Z","fulldoi":"https://doi.org/10.1016/j.jfa.2024.110495","date_created":"2024-05-26T22:00:57Z","file":[{"success":1,"date_updated":"2025-06-24T13:14:21Z","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","date_created":"2025-06-24T13:14:21Z","access_level":"open_access","file_size":1374854,"file_id":"19891","checksum":"07d3f73e0c56e68eb110851842c22ee0","relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"publication":"Journal of Functional Analysis","publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"status":"public","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"day":"15","file_date_updated":"2025-06-24T13:14:21Z","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"language":[{"iso":"eng"}],"OA_type":"hybrid","external_id":{"isi":["001325502400001"]},"abstract":[{"text":"We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between.","lang":"eng"}],"ec_funded":1,"issue":"4","article_number":"110495","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Elsevier","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110495.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” Journal of Functional Analysis, vol. 287, no. 4. Elsevier, 2024.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 287, no. 4, 110495, Elsevier, 2024, doi:10.1016/j.jfa.2024.110495.","ama":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 2024;287(4). doi:10.1016/j.jfa.2024.110495","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., & Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110495","short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024)."},"scopus_import":"1","_id":"17049","department":[{"_id":"LaEr"}]},{"month":"10","oa":1,"title":"Universality in low-dimensional BCS theory","article_processing_charge":"Yes (in subscription journal)","OA_place":"publisher","date_published":"2024-10-01T00:00:00Z","doi":"10.1142/s0129055x2360005x","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","oa_version":"Published Version","article_type":"original","has_accepted_license":"1","corr_author":"1","year":"2024","type":"journal_article","file":[{"checksum":"2b053a4223b4db14b90520999ec56054","file_id":"18786","file_size":503910,"access_level":"open_access","date_created":"2025-01-09T07:56:28Z","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","success":1,"date_updated":"2025-01-09T07:56:28Z","content_type":"application/pdf","creator":"dernst","relation":"main_file"}],"fulldoi":"https://doi.org/10.1142/s0129055x2360005x","date_created":"2023-11-15T23:48:14Z","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"publication_status":"published","publication":"Reviews in Mathematical Physics","date_updated":"2026-07-29T13:18:16Z","intvolume":" 36","isi":1,"volume":36,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18135"},{"relation":"dissertation_contains","status":"public","id":"19540"}]},"arxiv":1,"OA_type":"hybrid","abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["2301.05621"],"isi":["001099640300002"]},"status":"public","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"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"}],"language":[{"iso":"eng"}],"day":"01","file_date_updated":"2025-01-09T07:56:28Z","publisher":"World Scientific Publishing","_id":"14542","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"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.","citation":{"apa":"Henheik, S. J., Lauritsen, A. B., & Roos, B. (2024). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:10.1142/s0129055x2360005x.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics, vol. 36, no. 9. World Scientific Publishing, 2024.","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2024;36(9). doi:10.1142/s0129055x2360005x","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2024. https://doi.org/10.1142/s0129055x2360005x.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005."},"ec_funded":1,"article_number":"2360005 ","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"9"},{"publisher":"International Press of Boston","acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics. International Press of Boston, 2024. https://doi.org/10.4310/ATMP.241031013250.","ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083. doi:10.4310/ATMP.241031013250","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6. International Press of Boston, pp. 2025–2083, 2024.","mla":"Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International Press of Boston, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083.","apa":"Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. International Press of Boston. https://doi.org/10.4310/ATMP.241031013250"},"das_tickbox":"1","scopus_import":"1","_id":"18656","department":[{"_id":"LaEr"}],"ec_funded":1,"issue":"6","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"OA_type":"green","external_id":{"arxiv":["2402.17609"]},"abstract":[{"lang":"eng","text":"We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11])."}],"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"status":"public","day":"30","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"}],"language":[{"iso":"eng"}],"year":"2024","type":"journal_article","date_updated":"2026-07-29T13:18:17Z","fulldoi":"https://doi.org/10.4310/ATMP.241031013250","date_created":"2024-12-15T23:01:51Z","publication_identifier":{"eissn":["1095-0753"],"issn":["1095-0761"]},"publication":"Advances in Theoretical and Mathematical Physics","publication_status":"published","intvolume":" 28","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"volume":28,"oa":1,"month":"10","article_processing_charge":"No","title":"Out-of-time-ordered correlators for Wigner matrices","doi":"10.4310/ATMP.241031013250","OA_place":"repository","date_published":"2024-10-30T00:00:00Z","page":"2025-2083","corr_author":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.17609"}],"quality_controlled":"1","oa_version":"Preprint","article_type":"original"},{"day":"03","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Volodymyr","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov"}],"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"status":"public","external_id":{"arxiv":["2410.06813"]},"abstract":[{"lang":"eng","text":"For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes."}],"arxiv":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","ec_funded":1,"acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","citation":{"short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","apa":"Erdös, L., Henheik, S. J., & Riabov, V. (n.d.). Cusp universality for correlated random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.06813","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv. doi:10.48550/arXiv.2410.06813","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.06813.","ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” arXiv. .","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.06813.","ista":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, 10.48550/arXiv.2410.06813."},"department":[{"_id":"LaEr"}],"_id":"19547","corr_author":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.06813"}],"oa_version":"Preprint","doi":"10.48550/arXiv.2410.06813","OA_place":"repository","date_published":"2024-11-03T00:00:00Z","article_processing_charge":"No","title":"Cusp universality for correlated random matrices","oa":1,"month":"11","related_material":{"record":[{"relation":"later_version","status":"public","id":"20322"},{"relation":"dissertation_contains","id":"20575","status":"public"},{"id":"19540","status":"public","relation":"dissertation_contains"}]},"date_updated":"2026-07-29T13:18:17Z","fulldoi":"https://doi.org/10.48550/arXiv.2410.06813","date_created":"2025-04-11T08:48:21Z","publication":"arXiv","publication_status":"draft","year":"2024","type":"preprint"},{"OA_place":"repository","date_published":"2024-10-14T00:00:00Z","status":"public","doi":"10.48550/arXiv.2410.10809","author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"last_name":"Wessel","full_name":"Wessel, Tom","first_name":"Tom"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10809","open_access":"1"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"day":"14","corr_author":"1","month":"10","oa":1,"arxiv":1,"title":"Response theory for locally gapped systems","abstract":[{"text":"We introduce a notion of a \\emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings.\r\nOn a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system.\r\nMore precisely, we say that an equilibrium state ρ0 of a Hamiltonian H0 is locally gapped in Λgap⊂Λ, whenever the Liouvillian −i[H0,⋅] is almost invertible on local observables supported in Λgap when tested in ρ0.\r\nTo put this into context, we provide other alternative notions of a local gap and discuss their relations.\r\nThe validity of response theory is based on the construction of \\emph{non-equilibrium almost stationary states} (NEASSs).\r\nBy controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \\(\\epsilon V\\) acts in a region which is further than |logϵ| away from the non-gapped region Λ∖Λgap.","lang":"eng"}],"external_id":{"arxiv":["2410.10809"]},"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"year":"2024","type":"preprint","date_created":"2025-04-11T11:54:56Z","fulldoi":"https://doi.org/10.48550/arXiv.2410.10809","_id":"19551","publication":"arXiv","department":[{"_id":"LaEr"}],"publication_status":"draft","citation":{"short":"S.J. Henheik, T. Wessel, ArXiv (n.d.).","apa":"Henheik, S. J., & Wessel, T. (n.d.). Response theory for locally gapped systems. arXiv. https://doi.org/10.48550/arXiv.2410.10809","ieee":"S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” arXiv. .","mla":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” ArXiv, doi:10.48550/arXiv.2410.10809.","ama":"Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv. doi:10.48550/arXiv.2410.10809","chicago":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10809.","ista":"Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, 10.48550/arXiv.2410.10809."},"date_updated":"2026-07-29T13:18:16Z"},{"date_published":"2023-12-23T00:00:00Z","OA_place":"repository","doi":"10.48550/arXiv.2310.06677","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.06677","open_access":"1"}],"corr_author":"1","month":"12","oa":1,"title":"Prethermalization for deformed Wigner Matrices","article_processing_charge":"No","related_material":{"record":[{"relation":"later_version","status":"public","id":"18764"},{"relation":"dissertation_contains","status":"public","id":"20575"},{"id":"17164","status":"public","relation":"dissertation_contains"}]},"type":"preprint","year":"2023","publication":"arXiv","publication_status":"draft","date_created":"2024-06-26T08:56:52Z","fulldoi":"https://doi.org/10.48550/arXiv.2310.06677","date_updated":"2026-04-07T13:02:12Z","status":"public","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","last_name":"Reker"},{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov"}],"day":"23","arxiv":1,"external_id":{"arxiv":["2310.06677"]},"abstract":[{"lang":"eng","text":"We prove that a class of weakly perturbed Hamiltonians of the form $H_λ= H_0 + λW$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_λ$ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order $λ^{-2}$. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_λ$."}],"ec_funded":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_number":"2310.06677","department":[{"_id":"LaEr"}],"_id":"17174","citation":{"apa":"Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (n.d.). Prethermalization for deformed Wigner Matrices. arXiv. https://doi.org/10.48550/arXiv.2310.06677","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.).","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” ArXiv, 2310.06677, doi:10.48550/arXiv.2310.06677.","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner Matrices,” arXiv. .","ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv. doi:10.48550/arXiv.2310.06677","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2310.06677.","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv, 2310.06677."}}]