2003/04/30 by Christophe Texier, Pascal Degiovanni
Mathematics · Physics and Astronomy · #Graph theory and applications #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #cond-mat.mes-hall
paper · pdf · doi:10.1088/0305-4470/36/50/005
published as J.Phys.A: Math.Gen.36 (2003) 12425-12452 · 30 pages, 8 figures, LaTeX; added references
arxiv created 2003/10/13 · openalex publication_date 2003/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.