Scattering theory on graphs
Mesoscale and Nanoscale Physics
2009-11-07 v1 Chaotic Dynamics
Abstract
We consider the scattering theory for the Schr\"odinger operator on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.
Cite
@article{arxiv.cond-mat/0107104,
title = {Scattering theory on graphs},
author = {Christophe Texier and Gilles Montambaux},
journal= {arXiv preprint arXiv:cond-mat/0107104},
year = {2009}
}
Comments
21 pages, LaTeX, 10 eps figures