[{"date_updated":"2023-12-13T13:02:44Z","year":"2023","citation":{"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>","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>","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>.","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.","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics (2023).","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>.","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics."},"isi":1,"external_id":{"arxiv":["1902.07330"],"isi":["001073177200001"]},"doi":"10.1007/s00220-023-04837-z","arxiv":1,"day":"29","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"}],"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).","_id":"14427","scopus_import":"1","author":[{"last_name":"Chen","first_name":"Jianyu","full_name":"Chen, Jianyu"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim"},{"full_name":"Zhang, Hong Kun","last_name":"Zhang","first_name":"Hong Kun"}],"publication_status":"epub_ahead","date_created":"2023-10-15T22:01:11Z","article_processing_charge":"No","department":[{"_id":"VaKa"}],"title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","quality_controlled":"1","ec_funded":1,"publisher":"Springer Nature","article_type":"original","date_published":"2023-09-29T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1902.07330","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Communications in Mathematical Physics","oa_version":"Preprint","project":[{"grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020"}],"month":"09","language":[{"iso":"eng"}]},{"month":"11","oa_version":"Published Version","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"date_published":"2023-11-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_id":"14477","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access","date_updated":"2023-10-31T12:21:39Z","file_name":"2023_CommMathPhysics_Brooks.pdf","content_type":"application/pdf","date_created":"2023-10-31T12:21:39Z","file_size":832375,"checksum":"1ae49b39247cb6b40ff75997381581b8"}],"title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","intvolume":"       404","publication_status":"published","date_created":"2023-10-22T22:01:13Z","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","orcid":"0000-0002-6249-0928","last_name":"Brooks","first_name":"Morris"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"_id":"14441","scopus_import":"1","article_type":"original","publisher":"Springer Nature","file_date_updated":"2023-10-31T12:21:39Z","page":"287-337","quality_controlled":"1","ec_funded":1,"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."}],"arxiv":1,"doi":"10.1007/s00220-023-04841-3","day":"01","external_id":{"arxiv":["2207.03156"]},"date_updated":"2023-10-31T12:22:51Z","year":"2023","citation":{"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>.","short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","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.","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>","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>","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>.","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."},"ddc":["510"],"volume":404,"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)."},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_created":"2024-01-30T12:15:11Z","file_size":481209,"checksum":"cca204e81891270216a0c84eb8bcd398","date_updated":"2024-01-30T12:15:11Z","content_type":"application/pdf","file_name":"2023_CommMathPhysics_Vernooij.pdf","relation":"main_file","success":1,"access_level":"open_access","file_id":"14905","creator":"dernst"}],"oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_published":"2023-10-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"month":"10","oa_version":"Published Version","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","ddc":["510"],"volume":403,"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).","abstract":[{"lang":"eng","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."}],"arxiv":1,"doi":"10.1007/s00220-023-04795-6","day":"01","isi":1,"external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"date_updated":"2024-01-30T12:16:32Z","year":"2023","citation":{"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>.","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 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>","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>","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>.","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."},"article_type":"original","publisher":"Springer Nature","file_date_updated":"2024-01-30T12:15:11Z","page":"381-416","quality_controlled":"1","title":"Derivations and KMS-symmetric quantum Markov semigroups","intvolume":"       403","publication_status":"published","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JaMa"}],"date_created":"2023-07-30T22:01:03Z","author":[{"last_name":"Vernooij","first_name":"Matthijs","full_name":"Vernooij, Matthijs"},{"full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"_id":"13319","scopus_import":"1"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_updated":"2023-10-04T12:09:18Z","content_type":"application/pdf","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z","file_size":859967,"checksum":"72057940f76654050ca84a221f21786c","file_id":"14397","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access"}],"date_published":"2023-07-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","month":"07","oa_version":"Published Version","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"ddc":["510"],"volume":401,"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.","isi":1,"external_id":{"isi":["000957343500001"]},"date_updated":"2023-10-04T12:10:31Z","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 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>","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>","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.","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>."},"year":"2023","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"}],"doi":"10.1007/s00220-023-04692-y","day":"01","file_date_updated":"2023-10-04T12:09:18Z","page":"1665-1700","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Springer Nature","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"_id":"12792","scopus_import":"1","title":"On the spectral form factor for random matrices","intvolume":"       401","publication_status":"published","date_created":"2023-04-02T22:01:11Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)"},{"has_accepted_license":"1","publication":"Communications in Mathematical Physics","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"oa_version":"Published Version","month":"07","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2022-07-01T00:00:00Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa":1,"file":[{"date_updated":"2022-08-05T06:01:13Z","content_type":"application/pdf","file_name":"2022_CommunMathPhys_Schnelli.pdf","date_created":"2022-08-05T06:01:13Z","file_size":1141462,"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","creator":"dernst","access_level":"open_access","relation":"main_file","success":1}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","_id":"11332","author":[{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu"}],"article_processing_charge":"No","date_created":"2022-04-24T22:01:44Z","department":[{"_id":"LaEr"}],"publication_status":"published","intvolume":"       393","title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","ec_funded":1,"quality_controlled":"1","page":"839-907","file_date_updated":"2022-08-05T06:01:13Z","publisher":"Springer Nature","article_type":"original","year":"2022","citation":{"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>.","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.","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>","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.","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>."},"date_updated":"2023-08-03T06:34:24Z","external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"]},"isi":1,"day":"01","doi":"10.1007/s00220-022-04377-y","arxiv":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"}],"volume":393,"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.","ddc":["510"]},{"has_accepted_license":"1","publication":"Communications in Mathematical Physics","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"oa_version":"Published Version","month":"10","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2021-10-29T00:00:00Z","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"file":[{"content_type":"application/pdf","file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_updated":"2022-02-02T10:19:55Z","checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_size":841426,"date_created":"2022-02-02T10:19:55Z","creator":"cchlebak","file_id":"10715","access_level":"open_access","success":1,"relation":"main_file"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","_id":"10221","issue":"2","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"date_created":"2021-11-07T23:01:25Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","publication_status":"published","intvolume":"       388","title":"Eigenstate thermalization hypothesis for Wigner matrices","quality_controlled":"1","page":"1005–1048","file_date_updated":"2022-02-02T10:19:55Z","publisher":"Springer Nature","article_type":"original","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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>.","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.","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>.","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>","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>"},"year":"2021","date_updated":"2023-08-14T10:29:49Z","external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"isi":1,"day":"29","doi":"10.1007/s00220-021-04239-z","arxiv":1,"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"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","volume":388,"ddc":["510"]},{"publication":"Communications in Mathematical Physics","has_accepted_license":"1","month":"08","oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_published":"2021-08-30T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"creator":"cchlebak","file_id":"9990","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2021_CommunMathPhys_Wirth.pdf","date_updated":"2021-09-08T09:46:34Z","file_size":505971,"checksum":"8a602f916b1c2b0dc1159708b7cb204b","date_created":"2021-09-08T07:34:24Z"}],"author":[{"first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"last_name":"Zhang","first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"_id":"9973","scopus_import":"1","title":"Complete gradient estimates of quantum Markov semigroups","intvolume":"       387","publication_status":"published","department":[{"_id":"JaMa"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2021-08-30T10:07:44Z","file_date_updated":"2021-09-08T09:46:34Z","page":"761–791","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Springer Nature","isi":1,"external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"date_updated":"2023-08-11T11:09:07Z","citation":{"ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 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>.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","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>.","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.","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>","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>"},"year":"2021","abstract":[{"lang":"eng","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."}],"doi":"10.1007/s00220-021-04199-4","arxiv":1,"day":"30","ddc":["621"],"volume":387,"acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments."},{"has_accepted_license":"1","publication":"Communications in Mathematical Physics","project":[{"name":"FWF Open Access Fund","call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"oa_version":"Published Version","month":"03","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-03-01T00:00:00Z","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"file":[{"access_level":"open_access","relation":"main_file","file_id":"6668","creator":"dernst","date_created":"2019-07-24T07:19:10Z","file_size":853289,"checksum":"f9dd6dd615a698f1d3636c4a092fed23","date_updated":"2020-07-14T12:47:35Z","file_name":"2019_CommMathPhysics_Benedikter.pdf","content_type":"application/pdf"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","_id":"6649","author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","first_name":"Niels P","last_name":"Benedikter"},{"last_name":"Nam","first_name":"Phan Thành","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"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2019-07-18T13:30:04Z","article_processing_charge":"No","department":[{"_id":"RoSe"}],"publication_status":"published","intvolume":"       374","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","quality_controlled":"1","ec_funded":1,"page":"2097–2150","file_date_updated":"2020-07-14T12:47:35Z","publisher":"Springer Nature","article_type":"original","year":"2020","citation":{"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.","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>","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>","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.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","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>."},"date_updated":"2023-08-17T13:51:50Z","external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"isi":1,"day":"01","doi":"10.1007/s00220-019-03505-5","arxiv":1,"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"}],"volume":374,"ddc":["530"]},{"page":"1311-1395","ec_funded":1,"quality_controlled":"1","publisher":"Springer","article_type":"original","_id":"6906","scopus_import":"1","author":[{"full_name":"Boccato, Chiara","first_name":"Chiara","last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Brennecke, Christian","first_name":"Christian","last_name":"Brennecke"},{"first_name":"Serena","last_name":"Cenatiempo","full_name":"Cenatiempo, Serena"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"}],"publication_status":"published","department":[{"_id":"RoSe"}],"article_processing_charge":"No","date_created":"2019-09-24T17:30:59Z","title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","intvolume":"       376","volume":376,"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”.","date_updated":"2024-02-22T13:33:02Z","citation":{"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>.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","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.","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>","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>.","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."},"year":"2020","isi":1,"external_id":{"arxiv":["1812.03086"],"isi":["000536053300012"]},"arxiv":1,"doi":"10.1007/s00220-019-03555-9","day":"01","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."}],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","oa_version":"Preprint","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1812.03086"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2020-06-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa":1},{"language":[{"iso":"eng"}],"month":"06","project":[{"grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication":"Communications in Mathematical Physics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"type":"journal_article","date_published":"2020-06-01T00:00:00Z","article_type":"original","publisher":"Springer Nature","ec_funded":1,"quality_controlled":"1","page":"1803-1873","intvolume":"       376","title":"Cohomological Hall algebras, vertex algebras and instantons","department":[{"_id":"TaHa"}],"date_created":"2019-11-12T14:01:27Z","article_processing_charge":"No","publication_status":"published","author":[{"full_name":"Rapcak, Miroslav","first_name":"Miroslav","last_name":"Rapcak"},{"full_name":"Soibelman, Yan","first_name":"Yan","last_name":"Soibelman"},{"first_name":"Yaping","last_name":"Yang","full_name":"Yang, Yaping"},{"full_name":"Zhao, Gufang","first_name":"Gufang","last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"7004","volume":376,"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."}],"day":"01","doi":"10.1007/s00220-019-03575-5","arxiv":1,"external_id":{"isi":["000536255500004"],"arxiv":["1810.10402"]},"isi":1,"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>.","short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 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>","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>","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.","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>."},"year":"2020","date_updated":"2023-08-17T14:02:59Z"},{"abstract":[{"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).","lang":"eng"}],"day":"01","doi":"10.1007/s00220-019-03657-4","arxiv":1,"external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"isi":1,"year":"2020","citation":{"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>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","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.","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>","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>","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>.","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."},"date_updated":"2023-09-07T12:54:12Z","ddc":["530","510"],"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.","volume":378,"intvolume":"       378","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","department":[{"_id":"LaEr"}],"date_created":"2019-03-28T10:21:15Z","article_processing_charge":"Yes (via OA deal)","publication_status":"published","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"6185","article_type":"original","publisher":"Springer Nature","file_date_updated":"2020-11-18T11:14:37Z","ec_funded":1,"quality_controlled":"1","page":"1203-1278","oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"type":"journal_article","date_published":"2020-09-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"file":[{"creator":"dernst","file_id":"8771","relation":"main_file","access_level":"open_access","success":1,"file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","date_updated":"2020-11-18T11:14:37Z","checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_size":2904574,"date_created":"2020-11-18T11:14:37Z"}],"month":"09","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}]},{"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.08947"}],"oa":1,"publication_identifier":{"issn":["0010-3616","1432-0916"]},"date_published":"2019-05-09T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"month":"05","oa_version":"Preprint","publication":"Communications in Mathematical Physics","extern":"1","volume":374,"abstract":[{"lang":"eng","text":"We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit."}],"arxiv":1,"doi":"10.1007/s00220-019-03448-x","day":"09","external_id":{"arxiv":["1809.08947"]},"date_updated":"2021-01-12T08:19:08Z","year":"2019","citation":{"ista":"Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575.","mla":"Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:<a href=\"https://doi.org/10.1007/s00220-019-03448-x\">10.1007/s00220-019-03448-x</a>.","short":"P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575.","chicago":"Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03448-x\">https://doi.org/10.1007/s00220-019-03448-x</a>.","ieee":"P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019.","ama":"Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. 2019;374(3):1531-1575. doi:<a href=\"https://doi.org/10.1007/s00220-019-03448-x\">10.1007/s00220-019-03448-x</a>","apa":"Bálint, P., De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03448-x\">https://doi.org/10.1007/s00220-019-03448-x</a>"},"article_type":"original","publisher":"Springer Nature","page":"1531-1575","quality_controlled":"1","title":"Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards","intvolume":"       374","publication_status":"published","date_created":"2020-09-17T10:41:27Z","article_processing_charge":"No","author":[{"full_name":"Bálint, Péter","first_name":"Péter","last_name":"Bálint"},{"first_name":"Jacopo","last_name":"De Simoi","full_name":"De Simoi, Jacopo"},{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Martin","last_name":"Leguil","full_name":"Leguil, Martin"}],"issue":"3","_id":"8415"},{"ddc":["510"],"acknowledgement":"OA fund by IST Austria","volume":372,"abstract":[{"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.","lang":"eng"}],"doi":"10.1007/s00220-019-03599-x","day":"08","isi":1,"external_id":{"isi":["000495193700002"]},"date_updated":"2023-09-06T10:47:43Z","year":"2019","citation":{"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>","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>","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.","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>.","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69.","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>.","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."},"article_type":"original","publisher":"Springer Nature","file_date_updated":"2020-07-14T12:47:49Z","page":"1-69","ec_funded":1,"quality_controlled":"1","title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","intvolume":"       372","publication_status":"published","date_created":"2019-11-25T08:08:02Z","department":[{"_id":"RoSe"}],"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Jeblick, Maximilian","first_name":"Maximilian","last_name":"Jeblick"},{"full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","last_name":"Leopold","first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pickl","first_name":"Peter","full_name":"Pickl, Peter"}],"issue":"1","_id":"7100","scopus_import":"1","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"content_type":"application/pdf","file_name":"2019_CommMathPhys_Jeblick.pdf","date_updated":"2020-07-14T12:47:49Z","checksum":"cd283b475dd739e04655315abd46f528","file_size":884469,"date_created":"2019-11-25T08:11:11Z","creator":"dernst","file_id":"7101","access_level":"open_access","relation":"main_file"}],"oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"date_published":"2019-11-08T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"month":"11","oa_version":"Published Version","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1"},{"_id":"8417","publication":"Communications in Mathematical Physics","issue":"3","author":[{"last_name":"Delshams","first_name":"Amadeu","full_name":"Delshams, Amadeu"},{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"full_name":"de la Rosa, Abraham","last_name":"de la Rosa","first_name":"Abraham"},{"full_name":"Seara, Tere M.","first_name":"Tere M.","last_name":"Seara"}],"article_processing_charge":"No","date_created":"2020-09-17T10:41:43Z","publication_status":"published","oa_version":"None","intvolume":"       366","title":"Global instability in the restricted planar elliptic three body problem","month":"09","quality_controlled":"1","page":"1173-1228","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publisher":"Springer Nature","article_type":"original","citation":{"ama":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted planar elliptic three body problem. <i>Communications in Mathematical Physics</i>. 2018;366(3):1173-1228. doi:<a href=\"https://doi.org/10.1007/s00220-018-3248-z\">10.1007/s00220-018-3248-z</a>","apa":"Delshams, A., Kaloshin, V., de la Rosa, A., &#38; Seara, T. M. (2018). Global instability in the restricted planar elliptic three body problem. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-018-3248-z\">https://doi.org/10.1007/s00220-018-3248-z</a>","ieee":"A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability in the restricted planar elliptic three body problem,” <i>Communications in Mathematical Physics</i>, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.","chicago":"Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00220-018-3248-z\">https://doi.org/10.1007/s00220-018-3248-z</a>.","short":"A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228.","mla":"Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” <i>Communications in Mathematical Physics</i>, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:<a href=\"https://doi.org/10.1007/s00220-018-3248-z\">10.1007/s00220-018-3248-z</a>.","ista":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 366(3), 1173–1228."},"year":"2018","date_updated":"2021-01-12T08:19:08Z","type":"journal_article","date_published":"2018-09-05T00:00:00Z","publication_identifier":{"issn":["0010-3616","1432-0916"]},"day":"05","doi":"10.1007/s00220-018-3248-z","abstract":[{"text":"The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion.","lang":"eng"}],"volume":366,"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1"},{"page":"321-361","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","article_type":"original","_id":"8493","publication":"Communications in Mathematical Physics","author":[{"full_name":"Guardia, M.","last_name":"Guardia","first_name":"M."},{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"full_name":"Zhang, J.","first_name":"J.","last_name":"Zhang"}],"oa_version":"None","publication_status":"published","date_created":"2020-09-18T10:45:50Z","article_processing_charge":"No","month":"11","title":"A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems","intvolume":"       348","volume":348,"extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_updated":"2021-01-12T08:19:39Z","citation":{"apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2016). A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>","ama":"Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. 2016;348:321-361. doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems,” <i>Communications in Mathematical Physics</i>, vol. 348. Springer Nature, pp. 321–361, 2016.","chicago":"Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2016. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>.","short":"M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics 348 (2016) 321–361.","mla":"Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>, vol. 348, Springer Nature, 2016, pp. 321–61, doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>.","ista":"Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361."},"year":"2016","date_published":"2016-11-01T00:00:00Z","type":"journal_article","doi":"10.1007/s00220-016-2705-9","day":"01","publication_identifier":{"issn":["0010-3616","1432-0916"]},"abstract":[{"text":"In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.","lang":"eng"}]},{"publication_status":"published","department":[{"_id":"RoSe"}],"date_created":"2018-12-11T11:54:48Z","article_processing_charge":"No","title":"Formation of stripes and slabs near the ferromagnetic transition","intvolume":"       331","_id":"1935","scopus_import":"1","author":[{"last_name":"Giuliani","first_name":"Alessandro","full_name":"Giuliani, Alessandro"},{"full_name":"Lieb, Élliott","last_name":"Lieb","first_name":"Élliott"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"publisher":"Springer","article_type":"original","page":"333 - 350","quality_controlled":"1","file_date_updated":"2022-05-24T08:30:40Z","doi":"10.1007/s00220-014-1923-2","arxiv":1,"day":"01","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"}],"date_updated":"2022-05-24T08:32:50Z","citation":{"short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 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>.","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 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>","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>","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>.","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."},"year":"2014","external_id":{"arxiv":["1304.6344"]},"volume":331,"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.","ddc":["510"],"oa_version":"Published Version","month":"10","publication":"Communications in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa":1,"publist_id":"5159","date_published":"2014-10-01T00:00:00Z","type":"journal_article","file":[{"file_size":334064,"checksum":"c8423271cd1e1ba9e44c47af75efe7b6","date_created":"2022-05-24T08:30:40Z","file_name":"2014_CommMathPhysics_Giuliani.pdf","content_type":"application/pdf","date_updated":"2022-05-24T08:30:40Z","success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"11409"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public"},{"date_created":"2020-09-18T10:47:16Z","article_processing_charge":"No","publication_status":"published","oa_version":"None","intvolume":"       315","month":"11","title":"An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension","publication":"Communications in Mathematical Physics","_id":"8502","issue":"3","author":[{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"full_name":"Saprykina, Maria","last_name":"Saprykina","first_name":"Maria"}],"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","page":"643-697","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"day":"01","doi":"10.1007/s00220-012-1532-x","abstract":[{"text":"The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.","lang":"eng"}],"citation":{"mla":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” <i>Communications in Mathematical Physics</i>, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:<a href=\"https://doi.org/10.1007/s00220-012-1532-x\">10.1007/s00220-012-1532-x</a>.","short":"V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697.","ista":"Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 315(3), 643–697.","apa":"Kaloshin, V., &#38; Saprykina, M. (2012). An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-012-1532-x\">https://doi.org/10.1007/s00220-012-1532-x</a>","ama":"Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. <i>Communications in Mathematical Physics</i>. 2012;315(3):643-697. doi:<a href=\"https://doi.org/10.1007/s00220-012-1532-x\">10.1007/s00220-012-1532-x</a>","ieee":"V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension,” <i>Communications in Mathematical Physics</i>, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.","chicago":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2012. <a href=\"https://doi.org/10.1007/s00220-012-1532-x\">https://doi.org/10.1007/s00220-012-1532-x</a>."},"year":"2012","date_updated":"2021-01-12T08:19:44Z","type":"journal_article","date_published":"2012-11-01T00:00:00Z","volume":315,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","extern":"1"},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","publication_identifier":{"issn":["0010-3616"]},"publist_id":"4153","date_published":"2002-02-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"oa_version":"None","month":"02","publication":"Communications in Mathematical Physics","acknowledgement":"This work started during the first author’s visit at the Erwin Schrödinger Institute, Vienna.\r\nValuable discussions with T. Hoffmann-Ostenhof and M. Loss are gratefully acknowledged. The authors thank\r\nthe referee for careful reading and comments","volume":225,"extern":"1","arxiv":1,"doi":"10.1007/s002200100585","day":"01","abstract":[{"text":"We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A L 2loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov-Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L 2 estimate on a singular integral operator.","lang":"eng"}],"date_updated":"2023-07-18T08:57:54Z","year":"2002","citation":{"ieee":"L. Erdös and V. Vougalter, “Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields,” <i>Communications in Mathematical Physics</i>, vol. 225, no. 2. Springer, pp. 399–421, 2002.","chicago":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields.” <i>Communications in Mathematical Physics</i>. Springer, 2002. <a href=\"https://doi.org/10.1007/s002200100585\">https://doi.org/10.1007/s002200100585</a>.","apa":"Erdös, L., &#38; Vougalter, V. (2002). Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s002200100585\">https://doi.org/10.1007/s002200100585</a>","ama":"Erdös L, Vougalter V. Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. <i>Communications in Mathematical Physics</i>. 2002;225(2):399-421. doi:<a href=\"https://doi.org/10.1007/s002200100585\">10.1007/s002200100585</a>","ista":"Erdös L, Vougalter V. 2002. Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. Communications in Mathematical Physics. 225(2), 399–421.","mla":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields.” <i>Communications in Mathematical Physics</i>, vol. 225, no. 2, Springer, 2002, pp. 399–421, doi:<a href=\"https://doi.org/10.1007/s002200100585\">10.1007/s002200100585</a>.","short":"L. Erdös, V. Vougalter, Communications in Mathematical Physics 225 (2002) 399–421."},"external_id":{"arxiv":["math-ph/0109015v1"]},"publisher":"Springer","article_type":"original","page":"399 - 421","quality_controlled":"1","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T11:59:21Z","title":"Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields","intvolume":"       225","_id":"2739","scopus_import":"1","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"full_name":"Vougalter, Vitali","last_name":"Vougalter","first_name":"Vitali"}],"issue":"2"},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/cond-mat/0005026"}],"type":"journal_article","date_published":"2001-11-01T00:00:00Z","oa":1,"publist_id":"4579","publication_identifier":{"issn":["0010-3616"]},"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","month":"11","oa_version":"Published Version","extern":"1","volume":224,"external_id":{"arxiv":["cond-mat/0005026"]},"year":"2001","citation":{"chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” <i>Communications in Mathematical Physics</i>. Springer, 2001. <a href=\"https://doi.org/10.1007/s002200100533\">https://doi.org/10.1007/s002200100533</a>.","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas,” <i>Communications in Mathematical Physics</i>, vol. 224, no. 1. Springer, pp. 17–31, 2001.","ama":"Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. <i>Communications in Mathematical Physics</i>. 2001;224(1):17-31. doi:<a href=\"https://doi.org/10.1007/s002200100533\">10.1007/s002200100533</a>","apa":"Lieb, É., Seiringer, R., &#38; Yngvason, J. (2001). A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s002200100533\">https://doi.org/10.1007/s002200100533</a>","ista":"Lieb É, Seiringer R, Yngvason J. 2001. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications in Mathematical Physics. 224(1), 17–31.","mla":"Lieb, Élliott, et al. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” <i>Communications in Mathematical Physics</i>, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:<a href=\"https://doi.org/10.1007/s002200100533\">10.1007/s002200100533</a>.","short":"É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 224 (2001) 17–31."},"date_updated":"2023-05-30T12:28:46Z","abstract":[{"lang":"eng","text":"We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̅a 2 is small, where ρ̅ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross–Pitaevskii (GP) energy functional with a coupling constant g~1/|1n(ρ̅a 2)|. In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas–Fermi type functional is adequate."}],"day":"01","arxiv":1,"doi":"10.1007/s002200100533","quality_controlled":"1","page":"17 - 31","article_type":"original","publisher":"Springer","issue":"1","author":[{"full_name":"Lieb, Élliott","first_name":"Élliott","last_name":"Lieb"},{"first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Yngvason, Jakob","first_name":"Jakob","last_name":"Yngvason"}],"scopus_import":"1","_id":"2347","intvolume":"       224","title":"A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas","article_processing_charge":"No","date_created":"2018-12-11T11:57:08Z","publication_status":"published"},{"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","oa_version":"Preprint","month":"02","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0010005","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2001-02-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0010-3616"]},"oa":1,"publist_id":"4578","page":"229 - 248","quality_controlled":"1","publisher":"Springer","article_type":"original","_id":"2348","scopus_import":"1","author":[{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"1","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T11:57:08Z","title":"A discrete density matrix theory for atoms in strong magnetic fields","intvolume":"       217","volume":217,"acknowledgement":"The authors would like to thank Bernhard Baumgartner and Jakob Yngvason for proofreading and valuable comments.","extern":"1","date_updated":"2023-05-30T06:54:54Z","citation":{"short":"C. Hainzl, R. Seiringer, Communications in Mathematical Physics 217 (2001) 229–248.","mla":"Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory for Atoms in Strong Magnetic Fields.” <i>Communications in Mathematical Physics</i>, vol. 217, no. 1, Springer, 2001, pp. 229–48, doi:<a href=\"https://doi.org/10.1007/s002200100373\">10.1007/s002200100373</a>.","ista":"Hainzl C, Seiringer R. 2001. A discrete density matrix theory for atoms in strong magnetic fields. Communications in Mathematical Physics. 217(1), 229–248.","apa":"Hainzl, C., &#38; Seiringer, R. (2001). A discrete density matrix theory for atoms in strong magnetic fields. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s002200100373\">https://doi.org/10.1007/s002200100373</a>","ama":"Hainzl C, Seiringer R. A discrete density matrix theory for atoms in strong magnetic fields. <i>Communications in Mathematical Physics</i>. 2001;217(1):229-248. doi:<a href=\"https://doi.org/10.1007/s002200100373\">10.1007/s002200100373</a>","ieee":"C. Hainzl and R. Seiringer, “A discrete density matrix theory for atoms in strong magnetic fields,” <i>Communications in Mathematical Physics</i>, vol. 217, no. 1. Springer, pp. 229–248, 2001.","chicago":"Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory for Atoms in Strong Magnetic Fields.” <i>Communications in Mathematical Physics</i>. Springer, 2001. <a href=\"https://doi.org/10.1007/s002200100373\">https://doi.org/10.1007/s002200100373</a>."},"year":"2001","external_id":{"arxiv":["math-ph/0010005"]},"doi":"10.1007/s002200100373","arxiv":1,"day":"01","abstract":[{"text":"This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy.","lang":"eng"}]}]