---
res:
bibo_abstract:
- "In the customary random matrix model for transport in quantum dots with M internal
degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C 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 \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C 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
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: Erdös, László
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Torben H
foaf_name: Krüger, Torben H
foaf_surname: Krüger
foaf_workInfoHomepage: http://www.librecat.org/personId=3020C786-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4821-3297
- foaf_Person:
foaf_givenName: Yuriy
foaf_name: Nemish, Yuriy
foaf_surname: Nemish
foaf_workInfoHomepage: http://www.librecat.org/personId=4D902E6A-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-7327-856X
bibo_doi: 10.1007/s00023-021-01085-6
bibo_volume: 22
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1424-0637
- http://id.crossref.org/issn/1424-0661
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Scattering in quantum dots via noncommutative rational functions@
...