Charge and current distribution in graphs

Christophe Texier 1, 2, Pascal Degiovanni 3

Journal of Physics A 36 (2003) 12425-12452

We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.

  • 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
  • 3. Laboratoire de Physique de l'ENS Lyon (Phys-ENS),
    CNRS : UMR5672 – École Normale Supérieure - Lyon