English

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 \Dcx2+V(x)-\Dc_x^2+V(x) 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.

Keywords

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