@article{9912,
abstract = {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.},
author = {Erdös, László and Krüger, Torben H and Nemish, Yuriy},
issn = {1424-0661},
journal = {Annales Henri Poincaré },
pages = {4205–4269},
publisher = {Springer Nature},
title = {{Scattering in quantum dots via noncommutative rational functions}},
doi = {10.1007/s00023-021-01085-6},
volume = {22},
year = {2021},
}