An approximation to ${\delta }^{\prime }$ couplings on graphs

Abstract

We discuss a general parametrization for vertices of quantum graphs and show, in particular, how the ${\delta }_s^{\prime }$ and ${\delta }^{\prime }$ coupling at an $n$ edge vertex can be approximated by means of $n+1$ couplings of the $\delta$ type provided the latter are properly scaled.

arXiv comment10 pages, LaTeX, 1 figure added, to be published in J. of Phys. A

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Cited by in corpus (22)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Approximation of a general singular vertex coupling in quantum graphs
• Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide
• Leaky Quantum Graphs: A Review
• Spectral Theory of Infinite Quantum Graphs
• Approximations of singular vertex couplings in quantum graphs
• A remark on Krein's resolvent formula and boundary conditions
• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
• A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
• Non-Weyl asymptotics for quantum graphs with general coupling conditions
• The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
• Schrödinger operators with singular rank-two perturbations and point interactions
• Quantum Abacus
• On ${\delta }^{\prime }$-like potential scattering on star graphs
• Two-parametric ${\delta }^{\prime }$-interactions: approximation by Schrödinger operators with localized rank-two perturbations
• Tripartite connection condition for quantum graph vertex
• Reducible boundary conditions in coupled channels
• Dynamical and variational properties of the NLS-${\delta }_s^{\prime }$ equation on the star graph
• Quantum graphs: Coulomb-type potentials and exactly solvable models
• Vertex coupling in quantum graphs: approximations by scaled Schroedinger operators
• On negative eigenvalues of 1D Schrödinger operators with ${\delta }^{\prime }$-like potentials
• Spin filtering on a ring with Rashba hamiltonian