Reducible boundary conditions in coupled channels

2005/06/30 by Konstantin Pankrashkin · 6 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Geometry #Mathematical analysis #Mathematics #Physics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math-ph #math.MP #msc:15A90 #msc:34L30 #msc:47B25

paper · pdf · doi:10.1088/0305-4470/38/41/010

published in Journal of Physics A Mathematical and General 38(41), 8979-8992 (Institute of Physics) · 14 pages, to appear in J. Phys. A: Math. Gen

arxiv created 2005/09/07 · openalex publication_date 2005/09/28 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs, we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. It shown that such a reduction is closely connected with the invariance under channel permutations. Examples are provided by some 'model' interactions, in particular, the so-called δ, δ' and the Kirchhoff couplings.

Citations

• Kirchhoff's rule for quantum wires
• Continuous Spectra of Generalized Kronig–Penney Model
• A remark on Krein's resolvent formula and boundary conditions
• The generalized point interaction in one dimension
• A New Class of Point Interactions in One Dimension
• Convergence of spectra of graph-like thin manifolds