[{"oa_version":"Preprint","abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"month":"01","intvolume":" 63","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2012.15238"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"publication_status":"published","volume":63,"issue":"1","ec_funded":1,"_id":"10600","status":"public","keyword":["mathematical physics","statistical and nonlinear physics"],"article_type":"original","type":"journal_article","date_updated":"2023-08-02T13:44:32Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","quality_controlled":"1","publisher":"AIP Publishing","oa":1,"day":"03","publication":"Journal of Mathematical Physics","isi":1,"year":"2022","date_published":"2022-01-03T00:00:00Z","doi":"10.1063/5.0051632","date_created":"2022-01-03T12:19:48Z","article_number":"011901","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63, no. 1. AIP Publishing, 2022.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901."},"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"}],"article_processing_charge":"No","external_id":{"arxiv":["2012.15238"],"isi":["000739446000009"]}},{"date_published":"2022-01-18T00:00:00Z","doi":"10.1007/s11005-021-01494-y","date_created":"2022-01-18T16:18:25Z","day":"18","publication":"Letters in Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2022","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"},{"last_name":"Wessel","full_name":"Wessel, Tom","first_name":"Tom"}],"external_id":{"arxiv":["2106.13780"],"isi":["000744930400001"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.","ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y.","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","apa":"Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"9","issue":"1","volume":112,"ec_funded":1,"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"7e8e69b76e892c305071a4736131fe18","file_id":"10647","creator":"cchlebak","file_size":357547,"date_updated":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","date_created":"2022-01-19T09:41:14Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"publication_status":"published","month":"01","intvolume":" 112","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences."}],"file_date_updated":"2022-01-19T09:41:14Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ddc":["530"],"date_updated":"2023-08-02T13:57:02Z","status":"public","keyword":["mathematical physics","statistical and nonlinear physics"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10642"},{"ec_funded":1,"volume":10,"publication_status":"published","publication_identifier":{"eissn":["2050-5094"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf","date_updated":"2022-01-19T09:27:43Z","file_size":705323,"creator":"cchlebak","checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"intvolume":" 10","month":"01","abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"oa_version":"Published Version","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:27:43Z","date_updated":"2023-08-02T13:53:11Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"status":"public","_id":"10643","date_created":"2022-01-18T16:18:51Z","date_published":"2022-01-18T00:00:00Z","doi":"10.1017/fms.2021.80","year":"2022","has_accepted_license":"1","isi":1,"publication":"Forum of Mathematics, Sigma","day":"18","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"article_processing_charge":"Yes","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","citation":{"short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_number":"e4"},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_number":"3","title":"The BCS critical temperature at high density","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0","ama":"Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","date_created":"2022-01-13T15:40:53Z","date_published":"2022-01-11T00:00:00Z","doi":"10.1007/s11040-021-09415-0","publication":"Mathematical Physics, Analysis and Geometry","day":"11","year":"2022","isi":1,"has_accepted_license":"1","keyword":["geometry and topology","mathematical physics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"10623","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z","ddc":["514"],"date_updated":"2023-08-02T13:51:52Z","intvolume":" 25","month":"01","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.","lang":"eng"}],"ec_funded":1,"issue":"1","volume":25,"language":[{"iso":"eng"}],"file":[{"checksum":"d44f8123a52592a75b2c3b8ee2cd2435","file_id":"10624","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2022-01-14T07:27:45Z","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_updated":"2022-01-14T07:27:45Z","file_size":505804,"creator":"cchlebak"}],"publication_status":"published","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]}},{"article_number":"109394","title":"Thermalisation for Wigner matrices","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394."},"quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","date_published":"2022-04-15T00:00:00Z","doi":"10.1016/j.jfa.2022.109394","date_created":"2022-02-06T23:01:30Z","day":"15","publication":"Journal of Functional Analysis","has_accepted_license":"1","isi":1,"year":"2022","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10732","file_date_updated":"2022-07-29T07:22:08Z","department":[{"_id":"LaEr"}],"ddc":["500"],"date_updated":"2023-08-02T14:12:35Z","month":"04","intvolume":" 282","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"issue":"8","volume":282,"file":[{"creator":"dernst","date_updated":"2022-07-29T07:22:08Z","file_size":652573,"date_created":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"publication_status":"published"},{"citation":{"short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:10.1142/s2010326322500368.","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications. World Scientific, 2022. https://doi.org/10.1142/s2010326322500368."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Reker, Jana","last_name":"Reker","first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"article_processing_charge":"No","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"title":"On the operator norm of a Hermitian random matrix with correlated entries","article_number":"2250036","isi":1,"year":"2022","day":"01","publication":"Random Matrices: Theory and Applications","date_published":"2022-10-01T00:00:00Z","doi":"10.1142/s2010326322500368","date_created":"2022-04-08T07:11:12Z","quality_controlled":"1","publisher":"World Scientific","oa":1,"date_updated":"2023-08-03T06:32:22Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"_id":"11135","type":"journal_article","article_type":"original","status":"public","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":11,"issue":"4","abstract":[{"lang":"eng","text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"month":"10","intvolume":" 11"},{"has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Communications in Mathematical Physics","page":"839-907","date_published":"2022-07-01T00:00:00Z","doi":"10.1007/s00220-022-04377-y","date_created":"2022-04-24T22:01:44Z","acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"citation":{"chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” Communications in Mathematical Physics, vol. 393. Springer Nature, pp. 839–907, 2022.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y","apa":"Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"article_processing_charge":"No","external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"]},"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","success":1,"date_updated":"2022-08-05T06:01:13Z","file_size":1141462,"creator":"dernst","date_created":"2022-08-05T06:01:13Z","file_name":"2022_CommunMathPhys_Schnelli.pdf"}],"language":[{"iso":"eng"}],"volume":393,"ec_funded":1,"abstract":[{"text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"07","intvolume":" 393","date_updated":"2023-08-03T06:34:24Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-08-05T06:01:13Z","_id":"11332","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public"},{"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","year":"2022","isi":1,"publication":"Annals of Probability","day":"01","page":"984-1012","date_created":"2022-05-29T22:01:53Z","doi":"10.1214/21-AOP1552","date_published":"2022-05-01T00:00:00Z","citation":{"mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","abstract":[{"lang":"eng","text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2103.06730","open_access":"1"}],"scopus_import":"1","intvolume":" 50","month":"05","publication_status":"published","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"language":[{"iso":"eng"}],"issue":"3","volume":50,"_id":"11418","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-03T07:16:53Z","department":[{"_id":"LaEr"}]},{"publication_status":"published","publication_identifier":{"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2022_JourMathPhysics_Henheik.pdf","date_created":"2023-01-20T11:58:59Z","creator":"dernst","file_size":5436804,"date_updated":"2023-01-20T11:58:59Z","success":1,"file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"ec_funded":1,"volume":63,"issue":"12","abstract":[{"lang":"eng","text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"12","date_updated":"2023-08-03T14:12:01Z","ddc":["510"],"file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"_id":"12110","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Mathematical Physics","day":"01","date_created":"2023-01-08T23:00:53Z","doi":"10.1063/5.0104675","date_published":"2022-12-01T00:00:00Z","acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","oa":1,"publisher":"AIP Publishing","quality_controlled":"1","citation":{"mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675.","apa":"Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675.","ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000900748900002"]},"author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Roderich","last_name":"Tumulka","full_name":"Tumulka, Roderich"}],"title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","article_number":"122302","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}]},{"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"article_number":"e96","article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Rank-uniform local law for Wigner matrices","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","date_created":"2023-01-12T12:07:30Z","doi":"10.1017/fms.2022.86","date_published":"2022-10-27T00:00:00Z","year":"2022","has_accepted_license":"1","isi":1,"publication":"Forum of Mathematics, Sigma","day":"27","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"status":"public","_id":"12148","file_date_updated":"2023-01-24T10:02:40Z","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T09:00:35Z","ddc":["510"],"scopus_import":"1","intvolume":" 10","month":"10","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"oa_version":"Published Version","ec_funded":1,"volume":10,"publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"94a049aeb1eea5497aa097712a73c400","file_id":"12356","file_size":817089,"date_updated":"2023-01-24T10:02:40Z","creator":"dernst","file_name":"2022_ForumMath_Cipolloni.pdf","date_created":"2023-01-24T10:02:40Z"}]}]