Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles
Mesoscale and Nanoscale Physics
2009-11-11 v1
Abstract
In a quantum dot with three leads the transmission matrix t_{12} between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t_{12} becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t_{12}, which is related to a number of physical quantities. Changing the number of channels in the third lead corresponds to increasing the amount of loss in the system (and is distinct from prior uses of a third lead to model dephasing).
Cite
@article{arxiv.cond-mat/0511477,
title = {Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles},
author = {Steven H. Simon and Aris L. Moustakas},
journal= {arXiv preprint arXiv:cond-mat/0511477},
year = {2009}
}