Scattering theory on graphs

Christophe Texier 1, 2, Gilles Montambaux 2

Journal of Physics A 34 (2001) 10307-10326

We consider the scattering theory for the Schrödinger operator $-\Dc_x^2+V(x)$ 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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Laboratoire de Physique des Solides (LPS),
    CNRS : UMR8502 – Université Paris XI - Paris Sud