[{"day":"01","page":"1665-1700","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"license":"https://creativecommons.org/licenses/by/4.0/","has_accepted_license":"1","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Springer Nature","type":"journal_article","date_published":"2023-07-01T00:00:00Z","external_id":{"isi":["000957343500001"]},"ddc":["510"],"language":[{"iso":"eng"}],"status":"public","isi":1,"month":"07","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","article_type":"original","scopus_import":"1","doi":"10.1007/s00220-023-04692-y","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","file_date_updated":"2023-10-04T12:09:18Z","title":"On the spectral form factor for random matrices","publication_status":"published","abstract":[{"text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics.","lang":"eng"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>"},"year":"2023","file":[{"checksum":"72057940f76654050ca84a221f21786c","creator":"dernst","file_id":"14397","content_type":"application/pdf","date_created":"2023-10-04T12:09:18Z","relation":"main_file","file_size":859967,"date_updated":"2023-10-04T12:09:18Z","file_name":"2023_CommMathPhysics_Cipolloni.pdf","access_level":"open_access","success":1}],"date_created":"2023-04-02T22:01:11Z","_id":"12792","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"volume":401,"oa":1,"intvolume":"       401","date_updated":"2023-10-04T12:10:31Z","ec_funded":1,"publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}]},{"date_updated":"2024-01-30T12:16:32Z","publication":"Communications in Mathematical Physics","department":[{"_id":"JaMa"}],"intvolume":"       403","arxiv":1,"volume":403,"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Vernooij, Matthijs","first_name":"Matthijs","last_name":"Vernooij"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior"}],"file":[{"checksum":"cca204e81891270216a0c84eb8bcd398","content_type":"application/pdf","creator":"dernst","file_id":"14905","relation":"main_file","date_updated":"2024-01-30T12:15:11Z","date_created":"2024-01-30T12:15:11Z","file_size":481209,"success":1,"access_level":"open_access","file_name":"2023_CommMathPhysics_Vernooij.pdf"}],"date_created":"2023-07-30T22:01:03Z","_id":"13319","abstract":[{"text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule.","lang":"eng"}],"citation":{"ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>.","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>"},"year":"2023","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","file_date_updated":"2024-01-30T12:15:11Z","title":"Derivations and KMS-symmetric quantum Markov semigroups","publication_status":"published","acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00220-023-04795-6","status":"public","isi":1,"month":"10","ddc":["510"],"language":[{"iso":"eng"}],"type":"journal_article","external_id":{"isi":["001033655400002"],"arxiv":["2303.15949"]},"date_published":"2023-10-01T00:00:00Z","publisher":"Springer Nature","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","quality_controlled":"1","day":"01","page":"381-416"},{"arxiv":1,"date_updated":"2023-12-13T13:02:44Z","ec_funded":1,"publication":"Communications in Mathematical Physics","department":[{"_id":"VaKa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Chen","first_name":"Jianyu","full_name":"Chen, Jianyu"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim"},{"first_name":"Hong Kun","last_name":"Zhang","full_name":"Zhang, Hong Kun"}],"oa":1,"abstract":[{"text":"In the paper, we establish Squash Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls’ Barrier function from the maximal marked length spectrum associated to the rotation number 2n/4n+1.","lang":"eng"}],"citation":{"mla":"Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>.","chicago":"Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>.","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics (2023).","apa":"Chen, J., Kaloshin, V., &#38; Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>","ieee":"J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023.","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics.","ama":"Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>"},"year":"2023","date_created":"2023-10-15T22:01:11Z","_id":"14427","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"acknowledgement":"VK acknowledges a partial support by the NSF grant DMS-1402164 and ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very useful. JC visited the University of Maryland and thanks for the hospitality. Also, JC was partially supported by the National Key Research and Development Program of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850. H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211), as well as Simons Foundation Collaboration Grants for Mathematicians (706383).","article_type":"original","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"doi":"10.1007/s00220-023-04837-z","oa_version":"Preprint","article_processing_charge":"No","title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","publication_status":"epub_ahead","language":[{"iso":"eng"}],"status":"public","isi":1,"month":"09","publisher":"Springer Nature","type":"journal_article","date_published":"2023-09-29T00:00:00Z","external_id":{"arxiv":["1902.07330"],"isi":["001073177200001"]},"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}],"day":"29","quality_controlled":"1"},{"page":"287-337","day":"01","quality_controlled":"1","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"publisher":"Springer Nature","date_published":"2023-11-01T00:00:00Z","external_id":{"arxiv":["2207.03156"]},"type":"journal_article","language":[{"iso":"eng"}],"ddc":["510"],"month":"11","status":"public","doi":"10.1007/s00220-023-04841-3","scopus_import":"1","article_type":"original","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","publication_status":"published","title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","file_date_updated":"2023-10-31T12:21:39Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","year":"2023","citation":{"ama":"Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. 2023;404:287-337. doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>","ieee":"M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 287–337, 2023.","ista":"Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.","mla":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 287–337, doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>.","chicago":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>.","short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","apa":"Brooks, M., &#38; Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>"},"abstract":[{"lang":"eng","text":"We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation."}],"_id":"14441","date_created":"2023-10-22T22:01:13Z","file":[{"success":1,"access_level":"open_access","file_name":"2023_CommMathPhysics_Brooks.pdf","file_size":832375,"date_updated":"2023-10-31T12:21:39Z","date_created":"2023-10-31T12:21:39Z","relation":"main_file","creator":"dernst","file_id":"14477","content_type":"application/pdf","checksum":"1ae49b39247cb6b40ff75997381581b8"}],"author":[{"orcid":"0000-0002-6249-0928","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","first_name":"Morris","last_name":"Brooks"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"volume":404,"arxiv":1,"intvolume":"       404","department":[{"_id":"RoSe"}],"publication":"Communications in Mathematical Physics","ec_funded":1,"date_updated":"2023-10-31T12:22:51Z"},{"isi":1,"month":"07","status":"public","ddc":["510"],"language":[{"iso":"eng"}],"type":"journal_article","external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"]},"date_published":"2022-07-01T00:00:00Z","publisher":"Springer Nature","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"quality_controlled":"1","page":"839-907","day":"01","department":[{"_id":"LaEr"}],"ec_funded":1,"date_updated":"2023-08-03T06:34:24Z","publication":"Communications in Mathematical Physics","arxiv":1,"intvolume":"       393","volume":393,"oa":1,"author":[{"full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","last_name":"Schnelli","first_name":"Kevin"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","creator":"dernst","content_type":"application/pdf","date_created":"2022-08-05T06:01:13Z","date_updated":"2022-08-05T06:01:13Z","file_size":1141462,"relation":"main_file","success":1,"access_level":"open_access","file_name":"2022_CommunMathPhys_Schnelli.pdf"}],"date_created":"2022-04-24T22:01:44Z","_id":"11332","citation":{"ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. 2022;393:839-907. doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>","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.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 393. Springer Nature, pp. 839–907, 2022.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>.","apa":"Schnelli, K., &#38; Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 393, Springer Nature, 2022, pp. 839–907, doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>."},"year":"2022","abstract":[{"lang":"eng","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."}],"publication_status":"published","title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","article_processing_charge":"No","oa_version":"Published Version","file_date_updated":"2022-08-05T06:01:13Z","scopus_import":"1","doi":"10.1007/s00220-022-04377-y","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"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.","article_type":"original"},{"type":"journal_article","external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"date_published":"2021-10-29T00:00:00Z","publisher":"Springer Nature","status":"public","isi":1,"month":"10","ddc":["510"],"language":[{"iso":"eng"}],"quality_controlled":"1","day":"29","page":"1005–1048","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"issue":"2","volume":388,"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"date_updated":"2023-08-14T10:29:49Z","publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}],"intvolume":"       388","arxiv":1,"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2022-02-02T10:19:55Z","title":"Eigenstate thermalization hypothesis for Wigner matrices","publication_status":"published","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00220-021-04239-z","file":[{"relation":"main_file","date_created":"2022-02-02T10:19:55Z","file_size":841426,"date_updated":"2022-02-02T10:19:55Z","access_level":"open_access","success":1,"file_name":"2021_CommunMathPhys_Cipolloni.pdf","checksum":"a2c7b6f5d23b5453cd70d1261272283b","content_type":"application/pdf","file_id":"10715","creator":"cchlebak"}],"date_created":"2021-11-07T23:01:25Z","_id":"10221","abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021."},"year":"2021"},{"date_created":"2021-08-30T10:07:44Z","file":[{"checksum":"8a602f916b1c2b0dc1159708b7cb204b","creator":"cchlebak","file_id":"9990","content_type":"application/pdf","date_created":"2021-09-08T07:34:24Z","relation":"main_file","date_updated":"2021-09-08T09:46:34Z","file_size":505971,"file_name":"2021_CommunMathPhys_Wirth.pdf","access_level":"open_access"}],"_id":"9973","abstract":[{"text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.","lang":"eng"}],"citation":{"ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>."},"year":"2021","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2021-09-08T09:46:34Z","publication_status":"published","title":"Complete gradient estimates of quantum Markov semigroups","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00220-021-04199-4","ec_funded":1,"date_updated":"2023-08-11T11:09:07Z","publication":"Communications in Mathematical Physics","department":[{"_id":"JaMa"}],"intvolume":"       387","arxiv":1,"volume":387,"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior"},{"first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","quality_controlled":"1","day":"30","page":"761–791","status":"public","isi":1,"month":"08","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"ddc":["621"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2021-08-30T00:00:00Z","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"publisher":"Springer Nature"},{"article_type":"original","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"doi":"10.1007/s00220-019-03575-5","scopus_import":"1","article_processing_charge":"No","oa_version":"Preprint","publication_status":"published","title":"Cohomological Hall algebras, vertex algebras and instantons","abstract":[{"lang":"eng","text":"We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds."}],"year":"2020","citation":{"mla":"Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>.","apa":"Rapcak, M., Soibelman, Y., Yang, Y., &#38; Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>","chicago":"Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>.","short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","ama":"Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. 2020;376:1803-1873. doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>","ieee":"M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer Nature, pp. 1803–1873, 2020.","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873."},"_id":"7004","date_created":"2019-11-12T14:01:27Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Miroslav","last_name":"Rapcak","full_name":"Rapcak, Miroslav"},{"first_name":"Yan","last_name":"Soibelman","full_name":"Soibelman, Yan"},{"full_name":"Yang, Yaping","last_name":"Yang","first_name":"Yaping"},{"first_name":"Gufang","last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang"}],"oa":1,"volume":376,"intvolume":"       376","arxiv":1,"publication":"Communications in Mathematical Physics","date_updated":"2023-08-17T14:02:59Z","ec_funded":1,"department":[{"_id":"TaHa"}],"day":"01","page":"1803-1873","quality_controlled":"1","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","grant_number":"320593"}],"publisher":"Springer Nature","date_published":"2020-06-01T00:00:00Z","external_id":{"arxiv":["1810.10402"],"isi":["000536255500004"]},"type":"journal_article","language":[{"iso":"eng"}],"status":"public","month":"06","isi":1},{"oa":1,"related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"volume":378,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"publication":"Communications in Mathematical Physics","ec_funded":1,"date_updated":"2023-09-07T12:54:12Z","department":[{"_id":"LaEr"}],"intvolume":"       378","arxiv":1,"file_date_updated":"2020-11-18T11:14:37Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","publication_status":"published","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","article_type":"original","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","doi":"10.1007/s00220-019-03657-4","scopus_import":"1","_id":"6185","date_created":"2019-03-28T10:21:15Z","file":[{"relation":"main_file","date_updated":"2020-11-18T11:14:37Z","date_created":"2020-11-18T11:14:37Z","file_size":2904574,"file_name":"2020_CommMathPhysics_Erdoes.pdf","access_level":"open_access","success":1,"checksum":"c3a683e2afdcea27afa6880b01e53dc2","content_type":"application/pdf","file_id":"8771","creator":"dernst"}],"abstract":[{"lang":"eng","text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969)."}],"year":"2020","citation":{"ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>"},"external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"date_published":"2020-09-01T00:00:00Z","type":"journal_article","publisher":"Springer Nature","status":"public","month":"09","isi":1,"language":[{"iso":"eng"}],"ddc":["530","510"],"quality_controlled":"1","day":"01","page":"1203-1278","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Benedikter","first_name":"Niels P","full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1071-6091"},{"first_name":"Phan Thành","last_name":"Nam","full_name":"Nam, Phan Thành"},{"first_name":"Marcello","last_name":"Porta","full_name":"Porta, Marcello"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"oa":1,"volume":374,"intvolume":"       374","arxiv":1,"publication":"Communications in Mathematical Physics","date_updated":"2023-08-17T13:51:50Z","ec_funded":1,"department":[{"_id":"RoSe"}],"article_type":"original","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"doi":"10.1007/s00220-019-03505-5","scopus_import":"1","file_date_updated":"2020-07-14T12:47:35Z","oa_version":"Published Version","article_processing_charge":"No","publication_status":"published","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","abstract":[{"text":"While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n","lang":"eng"}],"year":"2020","citation":{"mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>"},"_id":"6649","file":[{"relation":"main_file","file_size":853289,"date_updated":"2020-07-14T12:47:35Z","date_created":"2019-07-24T07:19:10Z","file_name":"2019_CommMathPhysics_Benedikter.pdf","access_level":"open_access","checksum":"f9dd6dd615a698f1d3636c4a092fed23","creator":"dernst","file_id":"6668","content_type":"application/pdf"}],"date_created":"2019-07-18T13:30:04Z","publisher":"Springer Nature","external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"date_published":"2020-03-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"ddc":["530"],"status":"public","month":"03","isi":1,"day":"01","page":"2097–2150","quality_controlled":"1","project":[{"name":"FWF Open Access Fund","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","call_identifier":"FWF"},{"call_identifier":"FWF","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1"},{"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"quality_controlled":"1","page":"1311-1395","day":"01","isi":1,"month":"06","status":"public","language":[{"iso":"eng"}],"type":"journal_article","external_id":{"arxiv":["1812.03086"],"isi":["000536053300012"]},"date_published":"2020-06-01T00:00:00Z","publisher":"Springer","date_created":"2019-09-24T17:30:59Z","_id":"6906","citation":{"ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 376, 1311–1395.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer, pp. 1311–1395, 2020.","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. 2020;376:1311-1395. doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>.","mla":"Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer, 2020, pp. 1311–95, doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>."},"year":"2020","abstract":[{"lang":"eng","text":"We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential."}],"title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","publication_status":"published","article_processing_charge":"No","oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1812.03086","open_access":"1"}],"doi":"10.1007/s00220-019-03555-9","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"acknowledgement":"We would like to thank P. T. Nam and R. Seiringer for several useful discussions and\r\nfor suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”.","article_type":"original","department":[{"_id":"RoSe"}],"date_updated":"2024-02-22T13:33:02Z","ec_funded":1,"publication":"Communications in Mathematical Physics","arxiv":1,"intvolume":"       376","volume":376,"oa":1,"author":[{"first_name":"Chiara","last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","full_name":"Boccato, Chiara"},{"full_name":"Brennecke, Christian","last_name":"Brennecke","first_name":"Christian"},{"first_name":"Serena","last_name":"Cenatiempo","full_name":"Cenatiempo, Serena"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"doi":"10.1007/s00220-019-03599-x","scopus_import":"1","article_type":"original","acknowledgement":"OA fund by IST Austria","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","file_date_updated":"2020-07-14T12:47:49Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","year":"2019","citation":{"ista":"Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.","ieee":"M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.","ama":"Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. 2019;372(1):1-69. doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>","mla":"Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>.","apa":"Jeblick, M., Leopold, N. K., &#38; Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69.","chicago":"Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>."},"abstract":[{"lang":"eng","text":"We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics."}],"_id":"7100","file":[{"access_level":"open_access","file_name":"2019_CommMathPhys_Jeblick.pdf","file_size":884469,"date_updated":"2020-07-14T12:47:49Z","date_created":"2019-11-25T08:11:11Z","relation":"main_file","content_type":"application/pdf","file_id":"7101","creator":"dernst","checksum":"cd283b475dd739e04655315abd46f528"}],"date_created":"2019-11-25T08:08:02Z","author":[{"full_name":"Jeblick, Maximilian","last_name":"Jeblick","first_name":"Maximilian"},{"full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","last_name":"Leopold","first_name":"Nikolai K"},{"first_name":"Peter","last_name":"Pickl","full_name":"Pickl, Peter"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"volume":372,"intvolume":"       372","department":[{"_id":"RoSe"}],"publication":"Communications in Mathematical Physics","date_updated":"2023-09-06T10:47:43Z","ec_funded":1,"page":"1-69","day":"08","quality_controlled":"1","issue":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publisher":"Springer Nature","external_id":{"isi":["000495193700002"]},"date_published":"2019-11-08T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"ddc":["510"],"month":"11","isi":1,"status":"public"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Alessandro","last_name":"Giuliani","full_name":"Giuliani, Alessandro"},{"full_name":"Lieb, Élliott","first_name":"Élliott","last_name":"Lieb"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert"}],"volume":331,"oa":1,"intvolume":"       331","arxiv":1,"date_updated":"2022-05-24T08:32:50Z","publication":"Communications in Mathematical Physics","department":[{"_id":"RoSe"}],"acknowledgement":"2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\r\n\r\nThe research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G. and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part of a project started in collaboration with Joel Lebowitz, whom we thank for many useful discussions and for his constant encouragement.","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00220-014-1923-2","article_processing_charge":"No","oa_version":"Published Version","file_date_updated":"2022-05-24T08:30:40Z","title":"Formation of stripes and slabs near the ferromagnetic transition","publication_status":"published","abstract":[{"text":"We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p &gt; 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.","lang":"eng"}],"citation":{"ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. 2014;331:333-350. doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” <i>Communications in Mathematical Physics</i>, vol. 331. Springer, pp. 333–350, 2014.","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350.","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>, vol. 331, Springer, 2014, pp. 333–50, doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>.","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.","apa":"Giuliani, A., Lieb, É., &#38; Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>."},"year":"2014","date_created":"2018-12-11T11:54:48Z","file":[{"file_name":"2014_CommMathPhysics_Giuliani.pdf","access_level":"open_access","success":1,"date_updated":"2022-05-24T08:30:40Z","relation":"main_file","date_created":"2022-05-24T08:30:40Z","file_size":334064,"creator":"dernst","file_id":"11409","content_type":"application/pdf","checksum":"c8423271cd1e1ba9e44c47af75efe7b6"}],"_id":"1935","publisher":"Springer","type":"journal_article","external_id":{"arxiv":["1304.6344"]},"date_published":"2014-10-01T00:00:00Z","ddc":["510"],"language":[{"iso":"eng"}],"publist_id":"5159","status":"public","month":"10","day":"01","page":"333 - 350","quality_controlled":"1","has_accepted_license":"1"}]