{"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.","ec_funded":1,"intvolume":"        22","date_updated":"2023-08-11T10:31:48Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"status":"public","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"}],"day":"01","quality_controlled":"1","has_accepted_license":"1","external_id":{"isi":["000681531500001"],"arxiv":["1911.05112"]},"article_type":"original","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"}],"volume":22,"isi":1,"file_date_updated":"2022-05-12T12:50:27Z","language":[{"iso":"eng"}],"author":[{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","full_name":"Krüger, Torben H"},{"full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","first_name":"Yuriy","last_name":"Nemish","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"4205–4269","department":[{"_id":"LaEr"}],"publication":"Annales Henri Poincaré ","date_created":"2021-08-15T22:01:29Z","year":"2021","ddc":["510"],"file":[{"relation":"main_file","date_created":"2022-05-12T12:50:27Z","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","file_size":1162454,"content_type":"application/pdf","date_updated":"2022-05-12T12:50:27Z","creator":"dernst","checksum":"8d6bac0e2b0a28539608b0538a8e3b38","access_level":"open_access","success":1,"file_id":"11365"}],"article_processing_charge":"Yes (in subscription journal)","date_published":"2021-12-01T00:00:00Z","_id":"9912","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"doi":"10.1007/s00023-021-01085-6","title":"Scattering in quantum dots via noncommutative rational functions","month":"12","oa_version":"Published Version","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>.","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>","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>","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269."},"type":"journal_article","publisher":"Springer Nature","oa":1,"scopus_import":"1","publication_status":"published"}