[{"volume":23,"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-08-04T09:33:52Z","publication":"Annales Henri Poincaré","department":[{"_id":"LaEr"}],"intvolume":"        23","article_processing_charge":"No","oa_version":"Published Version","file_date_updated":"2023-01-27T11:06:47Z","title":"Density of small singular values of the shifted real Ginibre ensemble","publication_status":"published","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"article_type":"original","scopus_import":"1","doi":"10.1007/s00023-022-01188-8","file":[{"checksum":"5582f059feeb2f63e2eb68197a34d7dc","creator":"dernst","file_id":"12424","content_type":"application/pdf","date_created":"2023-01-27T11:06:47Z","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","relation":"main_file","success":1,"access_level":"open_access","file_name":"2022_AnnalesHenriP_Cipolloni.pdf"}],"date_created":"2023-01-16T09:50:26Z","_id":"12232","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002."},"year":"2022","type":"journal_article","external_id":{"isi":["000796323500001"]},"date_published":"2022-11-01T00:00:00Z","publisher":"Springer Nature","status":"public","isi":1,"month":"11","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"ddc":["510"],"language":[{"iso":"eng"}],"quality_controlled":"1","day":"01","page":"3981-4002","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","issue":"11"},{"quality_controlled":"1","day":"01","page":"4205–4269","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","grant_number":"338804","call_identifier":"FP7"}],"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"date_published":"2021-12-01T00:00:00Z","type":"journal_article","publisher":"Springer Nature","status":"public","month":"12","isi":1,"language":[{"iso":"eng"}],"ddc":["510"],"file_date_updated":"2022-05-12T12:50:27Z","oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","publication_status":"published","title":"Scattering in quantum dots via noncommutative rational functions","article_type":"original","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","doi":"10.1007/s00023-021-01085-6","scopus_import":"1","_id":"9912","file":[{"date_created":"2022-05-12T12:50:27Z","date_updated":"2022-05-12T12:50:27Z","relation":"main_file","file_size":1162454,"success":1,"access_level":"open_access","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","checksum":"8d6bac0e2b0a28539608b0538a8e3b38","content_type":"application/pdf","creator":"dernst","file_id":"11365"}],"date_created":"2021-08-15T22:01:29Z","abstract":[{"text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.","lang":"eng"}],"year":"2021","citation":{"short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature, pp. 4205–4269, 2021.","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>"},"oa":1,"volume":22,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","first_name":"Yuriy","last_name":"Nemish"}],"publication":"Annales Henri Poincaré ","ec_funded":1,"date_updated":"2023-08-11T10:31:48Z","department":[{"_id":"LaEr"}],"intvolume":"        22","arxiv":1},{"_id":"6788","date_created":"2019-08-11T21:59:21Z","file":[{"checksum":"b6dbf0d837d809293d449adf77138904","content_type":"application/pdf","file_id":"6801","creator":"dernst","date_created":"2019-08-12T12:05:58Z","relation":"main_file","file_size":681139,"date_updated":"2020-07-14T12:47:40Z","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","access_level":"open_access"}],"year":"2019","citation":{"mla":"Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>.","chicago":"Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>.","apa":"Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>","short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.","ama":"Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>","ieee":"N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019.","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508."},"abstract":[{"lang":"eng","text":"We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations."}],"title":"Mean-field dynamics for the Nelson model with fermions","publication_status":"published","file_date_updated":"2020-07-14T12:47:40Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","doi":"10.1007/s00023-019-00828-w","scopus_import":"1","article_type":"original","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"department":[{"_id":"RoSe"}],"publication":"Annales Henri Poincare","ec_funded":1,"date_updated":"2023-08-29T07:09:06Z","arxiv":1,"intvolume":"        20","oa":1,"volume":20,"author":[{"first_name":"Nikolai K","last_name":"Leopold","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K"},{"first_name":"Sören P","last_name":"Petrat","orcid":"0000-0002-9166-5889","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"10","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":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","page":"3471–3508","day":"01","month":"10","isi":1,"status":"public","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"isi":["000487036900008"],"arxiv":["1807.06781"]},"date_published":"2019-10-01T00:00:00Z","type":"journal_article","publisher":"Springer Nature"}]