Scattering theory on graphs

2001/07/05 by Christophe Texier, Gilles Montambaux · 2 citations
Mathematics · Physics and Astronomy · #Graph theory and applications #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #cond-mat.mes-hall #nlin.CD

paper · pdf · doi:10.1088/0305-4470/34/47/328

published as J. Phys. A: Math. Gen. 34 (2001) 10307-10326 · 21 pages, LaTeX, 10 eps figures

arxiv created 2001/07/05 · openalex publication_date 2001/11/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We consider the scattering theory for the Schrödinger operator −D x 2 + V ( x ) on the 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 with a few known examples.

Citations

• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Kirchhoff's rule for quantum wires

Cited by

• Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection
• Local Friedel sum rule on graphs