[{"quality_controlled":"1","page":"3981-4002","day":"01","issue":"11","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"date_published":"2022-11-01T00:00:00Z","external_id":{"isi":["000796323500001"]},"type":"journal_article","publisher":"Springer Nature","month":"11","isi":1,"status":"public","language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"publication_status":"published","title":"Density of small singular values of the shifted real Ginibre ensemble","file_date_updated":"2023-01-27T11:06:47Z","oa_version":"Published Version","article_processing_charge":"No","doi":"10.1007/s00023-022-01188-8","scopus_import":"1","article_type":"original","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"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.","_id":"12232","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","access_level":"open_access","success":1,"file_name":"2022_AnnalesHenriP_Cipolloni.pdf"}],"date_created":"2023-01-16T09:50:26Z","year":"2022","citation":{"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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","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>","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>.","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.","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.","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>"},"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"}],"oa":1,"volume":23,"author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"publication":"Annales Henri Poincaré","date_updated":"2023-08-04T09:33:52Z","intvolume":"        23"},{"publisher":"Springer Nature","date_published":"2021-12-01T00:00:00Z","external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"type":"journal_article","language":[{"iso":"eng"}],"ddc":["510"],"status":"public","month":"12","isi":1,"day":"01","page":"4205–4269","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"first_name":"Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","full_name":"Nemish, Yuriy"}],"oa":1,"volume":22,"intvolume":"        22","arxiv":1,"publication":"Annales Henri Poincaré ","date_updated":"2023-08-11T10:31:48Z","ec_funded":1,"department":[{"_id":"LaEr"}],"article_type":"original","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"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","file_date_updated":"2022-05-12T12:50:27Z","oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","title":"Scattering in quantum dots via noncommutative rational functions","publication_status":"published","abstract":[{"lang":"eng","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."}],"year":"2021","citation":{"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>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","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>.","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.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","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>"},"_id":"9912","file":[{"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","content_type":"application/pdf","file_id":"11365","creator":"dernst","date_created":"2022-05-12T12:50:27Z","relation":"main_file","date_updated":"2022-05-12T12:50:27Z","file_size":1162454,"success":1,"access_level":"open_access","file_name":"2021_AnnHenriPoincare_Erdoes.pdf"}],"date_created":"2021-08-15T22:01:29Z"},{"_id":"6788","date_created":"2019-08-11T21:59:21Z","file":[{"checksum":"b6dbf0d837d809293d449adf77138904","file_id":"6801","creator":"dernst","content_type":"application/pdf","relation":"main_file","date_created":"2019-08-12T12:05:58Z","file_size":681139,"date_updated":"2020-07-14T12:47:40Z","access_level":"open_access","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf"}],"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>.","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.","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>.","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":[{"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.","lang":"eng"}],"title":"Mean-field dynamics for the Nelson model with fermions","publication_status":"published","file_date_updated":"2020-07-14T12:47:40Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00023-019-00828-w","scopus_import":"1","article_type":"original","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"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"},{"last_name":"Petrat","first_name":"Sören P","full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"10","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","page":"3471–3508","day":"01","month":"10","isi":1,"status":"public","language":[{"iso":"eng"}],"ddc":["510"],"date_published":"2019-10-01T00:00:00Z","external_id":{"isi":["000487036900008"],"arxiv":["1807.06781"]},"type":"journal_article","publisher":"Springer Nature"}]