Fano resonances in stubbed quantum waveguides with impurities

We consider T–shaped, two–dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S–matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S–matrices of the various constituent segments of the device through the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bigstar$\end{document}–product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.