2002/11/25 by Christophe Texier, Μ. Büttiker, Markus Buttiker
Mathematics · Physics and Astronomy · #Chordal graph #Combinatorics #Geometry #Graph #Graph theory #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum mechanics #Scalar (mathematics) #Scattering #Simple (philosophy) #Spectral Theory in Mathematical Physics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.67.245410
published as Phys. Rev. B67 (2003) 245410. · 25 pages, LaTeX, 8 figures
arxiv created 2002/11/25 · openalex publication_date 2003/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities, and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.