--- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '22290' abstract: - lang: eng 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. 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.' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Edwin full_name: Langmann, Edwin last_name: Langmann - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: 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 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 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. ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” Annales Henri Poincaré. Springer Nature, 2026. ista: Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré. 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. short: S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026). das_tickbox: '1' dataavailabilitystatement: Data sharing is not applicable to this article as no new data were created or analyzed in this study. date_created: 2026-07-13T09:42:22Z date_published: 2026-06-29T00:00:00Z date_updated: 2026-07-13T11:34:08Z day: '29' ddc: - '500' department: - _id: LaEr - _id: RoSe doi: 10.1007/s00023-026-01706-y ec_funded: 1 external_id: arxiv: - '2409.17297' fulldoi: https://doi.org/10.1007/s00023-026-01706-y has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00023-026-01706-y month: '06' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Annales Henri Poincaré publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '19550' relation: earlier_version status: public researchdata_availability: not applicable scopus_import: '1' status: public supplementarymaterial: not applicable title: Multi-band superconductors have enhanced critical temperatures tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20925' 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.' 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). article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Cornelia full_name: Vogel, Cornelia id: 1cd0554a-ea28-11f0-9f40-ff76440883cd last_name: Vogel citation: 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 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 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. 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. 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. short: L. Erdös, S.J. Henheik, C. Vogel, Letters in Mathematical Physics 116 (2026). corr_author: '1' das_tickbox: '1' dataavailabilitystatement: The Matlab code used to generate the datasets of the provided examples is available from the corresponding author on request. date_created: 2026-01-04T23:01:33Z date_published: 2026-02-01T00:00:00Z date_updated: 2026-07-23T06:42:28Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s11005-025-02037-5 ec_funded: 1 external_id: pmid: - '41459414' file: - access_level: open_access checksum: f2021f8f6d38491948b94a7765a64d0b content_type: application/pdf creator: dernst date_created: 2026-07-23T06:42:01Z date_updated: 2026-07-23T06:42:01Z file_id: '22390' file_name: 2026_LettersMathPhysics_Erdoes.pdf file_size: 602526 relation: main_file success: 1 file_date_updated: 2026-07-23T06:42:01Z fulldoi: https://doi.org/10.1007/s11005-025-02037-5 has_accepted_license: '1' intvolume: ' 116' language: - iso: eng mathsc: - 60B20 - 82C10 month: '02' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: upon request scopus_import: '1' status: public supplementarymaterial: yes title: Normal typicality and dynamical typicality for a random block-band matrix model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 116 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20322' abstract: - lang: eng 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. 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). article_number: '253' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: 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 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 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. 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. ista: Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253. 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. short: L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025). corr_author: '1' date_created: 2025-09-10T05:38:17Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-025-05417-z external_id: arxiv: - '2410.06813' isi: - '001565019000005' file: - access_level: open_access checksum: abd32af7b8ca6dc5b9080823a433986b content_type: application/pdf creator: dernst date_created: 2025-09-10T07:48:21Z date_updated: 2025-09-10T07:48:21Z file_id: '20336' file_name: 2025_CommMathPhysics_Erdoes.pdf file_size: 1465827 relation: main_file success: 1 file_date_updated: 2025-09-10T07:48:21Z fulldoi: https://doi.org/10.1007/s00220-025-05417-z has_accepted_license: '1' intvolume: ' 406' isi: 1 issue: '10' language: - iso: eng month: '09' oa: 1 oa_version: Published Version publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '19547' relation: earlier_version status: public - id: '20575' relation: dissertation_contains status: public scopus_import: '1' status: public title: Cusp universality for correlated random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 406 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20478' abstract: - lang: eng 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.' 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: 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 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 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. 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. ista: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. 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. short: Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025). corr_author: '1' date_created: 2025-10-16T13:10:26Z date_published: 2025-09-20T00:00:00Z date_updated: 2026-06-18T18:23:40Z day: '20' ddc: - '500' department: - _id: LaEr doi: 10.1007/s00440-025-01422-4 ec_funded: 1 external_id: arxiv: - '2503.06549' isi: - '001574640900001' fulldoi: https://doi.org/10.1007/s00440-025-01422-4 isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00440-025-01422-4 month: '09' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Decorrelation transition in the Wigner minor process type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: repository OA_type: green _id: '22340' abstract: - lang: eng 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. article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Yunzhe full_name: Li, Yunzhe id: 41cb05d3-f128-11eb-9611-e4e2b3cfba31 last_name: Li - first_name: Amir full_name: Vig, Amir id: 49d58dd5-45f5-11ec-9f86-8ce1276989b9 last_name: Vig citation: ama: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv. doi:10.48550/ARXIV.2511.10398 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 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. ieee: S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville tori,” arXiv. . ista: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv, 10.48550/ARXIV.2511.10398. 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.). corr_author: '1' date_created: 2026-07-14T12:51:50Z date_published: 2025-11-13T00:00:00Z date_updated: 2026-07-20T14:58:23Z day: '13' department: - _id: VaKa - _id: LaEr doi: 10.48550/ARXIV.2511.10398 external_id: arxiv: - '2511.10398' fulldoi: https://doi.org/10.48550/ARXIV.2511.10398 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 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2511.10398 month: '11' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '22255' relation: dissertation_contains status: public status: public title: Spectral rigidity of Liouville tori tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18112' 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.' 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. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X 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 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 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. 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. ista: Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503. 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. short: S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503. corr_author: '1' date_created: 2024-09-22T22:01:43Z date_published: 2025-02-01T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1017/etds.2024.48 ec_funded: 1 external_id: isi: - '001308182000001' file: - access_level: open_access checksum: 650fe115d998fe0ac3a8d0c7519447c8 content_type: application/pdf creator: dernst date_created: 2025-01-13T08:51:40Z date_updated: 2025-01-13T08:51:40Z file_id: '18828' file_name: 2025_ErgodicTheory_Henheik.pdf file_size: 659100 relation: main_file success: 1 file_date_updated: 2025-01-13T08:51:40Z fulldoi: https://doi.org/10.1017/etds.2024.48 has_accepted_license: '1' intvolume: ' 45' isi: 1 issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 467-503 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Ergodic Theory and Dynamical Systems publication_identifier: eissn: - 1469-4417 issn: - 0143-3857 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Deformational rigidity of integrable metrics on the torus tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19001' 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. 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. article_number: '14' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: 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 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 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. ieee: L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” Letters in Mathematical Physics, vol. 115. Springer Nature, 2025. ista: Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14. 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. short: L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025). corr_author: '1' date_created: 2025-02-05T06:48:29Z date_published: 2025-01-30T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '30' ddc: - '510' department: - _id: LaEr doi: 10.1007/s11005-025-01904-5 ec_funded: 1 external_id: arxiv: - '2410.08108' isi: - '001409618800002' pmid: - '39896265' file: - access_level: open_access checksum: ee07edf5f85a6f2651926b2f8760af74 content_type: application/pdf creator: dernst date_created: 2025-02-05T07:01:40Z date_updated: 2025-02-05T07:01:40Z file_id: '19004' file_name: 2025_LettersMathPhysics_Erdoes.pdf file_size: 828335 relation: main_file success: 1 file_date_updated: 2025-02-05T07:01:40Z fulldoi: https://doi.org/10.1007/s11005-025-01904-5 has_accepted_license: '1' intvolume: ' 115' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Letters in Mathematical Physics publication_identifier: issn: - 1573-0530 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Loschmidt echo for deformed Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2025' ... --- OA_place: repository _id: '19546' abstract: - lang: eng 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." acknowledgement: Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv. doi:10.48550/arXiv.2410.10718 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 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. ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” arXiv. . ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, 10.48550/arXiv.2410.10718. mla: Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.10718. short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:34:49Z date_published: 2025-01-30T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '30' department: - _id: LaEr doi: 10.48550/arXiv.2410.10718 ec_funded: 1 external_id: arxiv: - '2410.10718' fulldoi: https://doi.org/10.48550/arXiv.2410.10718 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.10718 month: '01' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Eigenvector decorrelation for random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: publisher _id: '19540' abstract: - lang: eng 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). " alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: 'Henheik SJ. Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. 2025. doi:10.15479/AT-ISTA-19540' 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' 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.' ieee: 'S. J. Henheik, “Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems,” Institute of Science and Technology Austria, 2025.' ista: 'Henheik SJ. 2025. Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria.' 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.' short: 'S.J. Henheik, Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.' corr_author: '1' date_created: 2025-04-10T21:21:18Z date_published: 2025-04-10T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '10' ddc: - '519' degree_awarded: PhD department: - _id: GradSch - _id: LaEr doi: 10.15479/AT-ISTA-19540 doi_confirm: '1' ec_funded: 1 file: - access_level: closed checksum: b8477ae5578436c72c3bb4193ad34ac5 content_type: application/zip creator: shenheik date_created: 2025-04-10T21:14:18Z date_updated: 2025-04-10T21:14:18Z file_id: '19542' file_name: Henheik-Thesis_source_final.zip file_size: 4107587 relation: source_file - access_level: open_access checksum: e9fc0ea12ec46c9f71110c33217c4140 content_type: application/pdf creator: shenheik date_created: 2025-04-11T13:16:05Z date_updated: 2025-04-11T13:16:05Z file_id: '19553' file_name: Henheik-Thesis-pdfa_FINAL.pdf file_size: 9999492 relation: main_file success: 1 - access_level: closed checksum: f94580f86c785e7108eb116cd189e225 content_type: application/pdf creator: cchlebak date_created: 2025-04-23T14:10:27Z date_updated: 2025-04-23T14:10:27Z file_id: '19615' file_name: Henheik-Thesis-Volume1_print.pdf file_size: 13276442 relation: other - access_level: closed checksum: b927ead3c78020ffb32918911deedb74 content_type: application/pdf creator: cchlebak date_created: 2025-04-23T14:11:05Z date_updated: 2025-04-23T14:11:05Z file_id: '19616' file_name: Henheik-Thesis-Volume2_print.pdf file_size: 7628767 relation: other file_date_updated: 2025-04-23T14:11:05Z fulldoi: https://doi.org/10.15479/AT-ISTA-19540 has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '720' project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication_identifier: isbn: - 978-3-99078-057-2 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '14343' relation: part_of_dissertation status: public - id: '13317' relation: part_of_dissertation status: public - id: '11732' relation: part_of_dissertation status: public - id: '12184' relation: part_of_dissertation status: public - id: '14421' relation: part_of_dissertation status: public - id: '10623' relation: part_of_dissertation status: public - id: '18112' relation: part_of_dissertation status: public - id: '19001' relation: part_of_dissertation status: public - id: '10642' relation: part_of_dissertation status: public - id: '19545' relation: part_of_dissertation status: public - id: '19546' relation: part_of_dissertation status: public - id: '19550' relation: part_of_dissertation status: public - id: '19551' relation: part_of_dissertation status: public - id: '19552' relation: part_of_dissertation status: public - id: '14542' relation: part_of_dissertation status: public - id: '17049' relation: part_of_dissertation status: public - id: '18764' relation: part_of_dissertation status: public - id: '19547' relation: part_of_dissertation status: public - id: '19548' relation: part_of_dissertation status: public - id: '18656' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: 'Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '19548' abstract: - lang: eng text: "We consider the BCS energy gap „.T / (essentially given by „.T / \x19 \x81.T; p\x16/,\r\nthe BCS order parameter) at all temperatures 0 \x14 T \x14 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 ." 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" article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: 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 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 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. 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. ista: Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352. 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. short: S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352. corr_author: '1' date_created: 2025-04-11T09:19:28Z date_published: 2025-01-09T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '09' ddc: - '500' department: - _id: LaEr - _id: RoSe doi: 10.4171/JST/540 ec_funded: 1 external_id: arxiv: - '2312.11310' isi: - '001438931600009' file: - access_level: open_access checksum: f49e06e8dba819f7ad52a202e287ebca content_type: application/pdf creator: cchlebak date_created: 2025-04-11T09:13:31Z date_updated: 2025-04-11T09:13:31Z file_id: '19549' file_name: Henheik_JSpectralTheory_2025.pdf file_size: 779158 relation: main_file success: 1 file_date_updated: 2025-04-11T09:13:31Z fulldoi: https://doi.org/10.4171/JST/540 has_accepted_license: '1' intvolume: ' 15' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 305–352 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Journal of Spectral Theory publication_identifier: eissn: - 1664-0403 publication_status: published publisher: EMS Press quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Universal behavior of the BCS energy gap tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18764' 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. 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)." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov 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 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 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. 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. ista: Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 26, 1991–2033. 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. short: L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033. corr_author: '1' date_created: 2025-01-05T23:01:59Z date_published: 2025-06-01T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-024-01518-y ec_funded: 1 external_id: arxiv: - '2310.06677' isi: - '001385326500001' file: - access_level: open_access checksum: 49e6a934db540206f7eaa0c798553ded content_type: application/pdf creator: dernst date_created: 2025-06-25T05:38:34Z date_updated: 2025-06-25T05:38:34Z file_id: '19895' file_name: 2025_AnnalesHenriPoincare_Erdoes.pdf file_size: 977773 relation: main_file success: 1 file_date_updated: 2025-06-25T05:38:34Z fulldoi: https://doi.org/10.1007/s00023-024-01518-y has_accepted_license: '1' intvolume: ' 26' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1991-2033 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '17174' relation: earlier_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Prethermalization for deformed Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 26 year: '2025' ... --- OA_place: repository _id: '19552' 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." acknowledgement: "JH gratefully acknowledges partial financial support by the ERC Advanced\r\nGrant “RMTBeyond” No. 101020331." article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Bipul full_name: Poudyal, Bipul last_name: Poudyal - first_name: Roderich full_name: Tumulka, Roderich last_name: Tumulka 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 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 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. ieee: S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps remove the ultraviolet divergence problem,” arXiv. . ista: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv, 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. short: S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T12:07:25Z date_published: 2025-02-28T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '28' department: - _id: LaEr doi: 10.48550/arXiv.2409.00677 ec_funded: 1 external_id: arxiv: - '2409.00677' fulldoi: https://doi.org/10.48550/arXiv.2409.00677 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.00677 month: '02' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: How a space-time singularity helps remove the ultraviolet divergence problem type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: repository _id: '19545' abstract: - lang: eng 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." acknowledgement: Supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488 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 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. ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” arXiv. . ista: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, 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. short: G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:19:22Z date_published: 2024-12-17T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '17' department: - _id: LaEr doi: 10.48550/arXiv.2309.05488 ec_funded: 1 external_id: arxiv: - '2309.05488' fulldoi: https://doi.org/10.48550/arXiv.2309.05488 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2309.05488 month: '12' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Eigenstate thermalisation at the edge for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19550' abstract: - lang: eng 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." article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Edwin full_name: Langmann, Edwin last_name: Langmann - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv. doi:10.48550/arXiv.2409.17297 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 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. ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” arXiv. . ista: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, 10.48550/arXiv.2409.17297. 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.). corr_author: '1' date_created: 2025-04-11T11:43:58Z date_published: 2024-10-21T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '21' department: - _id: LaEr - _id: RoSe doi: 10.48550/arXiv.2409.17297 external_id: arxiv: - '2409.17297' fulldoi: https://doi.org/10.48550/arXiv.2409.17297 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.17297 month: '10' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '22290' relation: later_version status: public - id: '19540' relation: dissertation_contains status: public status: public title: Multi-band superconductors have enhanced critical temperatures tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '17049' abstract: - lang: eng 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. acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089." article_number: '110495' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: 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 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. 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. 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. short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024). corr_author: '1' date_created: 2024-05-26T22:00:57Z date_published: 2024-08-15T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '15' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.jfa.2024.110495 ec_funded: 1 external_id: isi: - '001325502400001' file: - access_level: open_access checksum: 07d3f73e0c56e68eb110851842c22ee0 content_type: application/pdf creator: dernst date_created: 2025-06-24T13:14:21Z date_updated: 2025-06-24T13:14:21Z file_id: '19891' file_name: 2025_JourFunctionalAnalysis_Cipolloni.pdf file_size: 1374854 relation: main_file success: 1 file_date_updated: 2025-06-24T13:14:21Z fulldoi: https://doi.org/10.1016/j.jfa.2024.110495 has_accepted_license: '1' intvolume: ' 287' isi: 1 issue: '4' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 287 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '14542' abstract: - lang: eng text: "It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit." 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. article_number: '2360005 ' article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2024;36(9). doi:10.1142/s0129055x2360005x 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 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. 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. ista: Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005. 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. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024). corr_author: '1' date_created: 2023-11-15T23:48:14Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '01' ddc: - '510' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' isi: - '001099640300002' file: - access_level: open_access checksum: 2b053a4223b4db14b90520999ec56054 content_type: application/pdf creator: dernst date_created: 2025-01-09T07:56:28Z date_updated: 2025-01-09T07:56:28Z file_id: '18786' file_name: 2024_ReviewsmathPhysics_Henheik.pdf file_size: 503910 relation: main_file success: 1 file_date_updated: 2025-01-09T07:56:28Z fulldoi: https://doi.org/10.1142/s0129055x2360005x has_accepted_license: '1' intvolume: ' 36' isi: 1 issue: '9' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Universality in low-dimensional BCS theory tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 36 year: '2024' ... --- OA_place: repository OA_type: green _id: '18656' 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])." acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: 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 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 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. 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. 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. 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. corr_author: '1' das_tickbox: '1' date_created: 2024-12-15T23:01:51Z date_published: 2024-10-30T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '30' department: - _id: LaEr doi: 10.4310/ATMP.241031013250 ec_funded: 1 external_id: arxiv: - '2402.17609' fulldoi: https://doi.org/10.4310/ATMP.241031013250 intvolume: ' 28' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2402.17609 month: '10' oa: 1 oa_version: Preprint page: 2025-2083 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Advances in Theoretical and Mathematical Physics publication_identifier: eissn: - 1095-0753 issn: - 1095-0761 publication_status: published publisher: International Press of Boston quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Out-of-time-ordered correlators for Wigner matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2024' ... --- OA_place: repository _id: '19547' 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." acknowledgement: "Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331." article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv. doi:10.48550/arXiv.2410.06813 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 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. ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” arXiv. . ista: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, 10.48550/arXiv.2410.06813. mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.06813. short: L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:48:21Z date_published: 2024-11-03T00:00:00Z date_updated: 2026-07-29T13:18:17Z day: '03' department: - _id: LaEr doi: 10.48550/arXiv.2410.06813 ec_funded: 1 external_id: arxiv: - '2410.06813' fulldoi: https://doi.org/10.48550/arXiv.2410.06813 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.06813 month: '11' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '20322' relation: later_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public status: public title: Cusp universality for correlated random matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19551' abstract: - lang: eng 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." article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Tom full_name: Wessel, Tom last_name: Wessel citation: ama: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv. doi:10.48550/arXiv.2410.10809 apa: Henheik, S. J., & Wessel, T. (n.d.). Response theory for locally gapped systems. arXiv. https://doi.org/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. ieee: S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” arXiv. . ista: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, 10.48550/arXiv.2410.10809. mla: Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” ArXiv, doi:10.48550/arXiv.2410.10809. short: S.J. Henheik, T. Wessel, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T11:54:56Z date_published: 2024-10-14T00:00:00Z date_updated: 2026-07-29T13:18:16Z day: '14' department: - _id: LaEr doi: 10.48550/arXiv.2410.10809 external_id: arxiv: - '2410.10809' fulldoi: https://doi.org/10.48550/arXiv.2410.10809 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.10809 month: '10' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Response theory for locally gapped systems tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '17174' 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 $H_λ$. article_number: '2310.06677' article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv. doi:10.48550/arXiv.2310.06677 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 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. ieee: L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner Matrices,” arXiv. . ista: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv, 2310.06677. mla: Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” ArXiv, 2310.06677, doi:10.48550/arXiv.2310.06677. short: L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2024-06-26T08:56:52Z date_published: 2023-12-23T00:00:00Z date_updated: 2026-04-07T13:02:12Z day: '23' department: - _id: LaEr doi: 10.48550/arXiv.2310.06677 ec_funded: 1 external_id: arxiv: - '2310.06677' fulldoi: https://doi.org/10.48550/arXiv.2310.06677 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2310.06677 month: '12' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '18764' relation: later_version status: public - id: '20575' relation: dissertation_contains status: public - id: '17164' relation: dissertation_contains status: public status: public title: Prethermalization for deformed Wigner Matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ...