2009/08/26 by Taksu Cheon, Pavel Exner, Ondřej Turek +1 · 12 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Combinatorics #Connection (principal bundle) #Geometry #Graph #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum graph #Quantum mechanics #Scattering #Spectral Theory in Mathematical Physics #Spectral properties #Topology (electrical circuits) #Vertex (graph theory) #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1143/jpsj.78.124004
published in Journal of the Physical Society of Japan 78(12), 124004 (Physical Society of Japan) · RevTeX JPSJ format, 7 pages, 10 figures
arxiv created 2009/08/26 · openalex publication_date 2009/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We examine scattering properties of singular vertex of degree n=2 and n=3, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a singular vertex with finite potentials. We show that proper identification of δ and δ' components in the connection condition between outgoing lines enables the designing of quantum spectral branch-filters.