TY - JOUR
AB - In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via ๐โช๐ channels, the density ๐ 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 ๐:=๐/๐โค1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit ๐โ0, we recover the formula for the density ๐ that Beenakker (Rev Mod Phys 69:731โ808, 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 Beenakkerโs formula persists for any ๐<1 but in the borderline case ๐=1 an anomalous ๐โ2/3 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.
AU - Erdรถs, Lรกszlรณ
AU - Krรผger, Torben H
AU - Nemish, Yuriy
ID - 9912
JF - Annales Henri Poincare
SN - 1424-0637
TI - Scattering in quantum dots via noncommutative rational functions
ER -