The free Dirac operator on compact and noncompact graphs

DOI10.1063/1.529025zbMath0699.47032OpenAlexW2008948826MaRDI QIDQ3477544

W. Bulla, Thomas Trenkler

Publication date: 1990

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529025

zbMATH Keywords

eigenvaluespoint defectscattering coefficientsbranching linebundle of half-lineseye-shaped structurefree Dirac operator defined on composite one-dimensionalfree Dirac operator defined on composite one-dimensional structures consisting of finitely many half-lines and intervalsself-adjoint extensions of the Dirac operatorstructures consisting of finitely many half-lines and intervalstransition conditions for the wave functions

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05) Quantum field theory on lattices (81T25) Scattering theory of linear operators (47A40) Miscellaneous applications of functional analysis (46N99)

Related Items (20)

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction ⋮ Spectral asymptotics and regularized traces for Dirac operators on a star-shaped graph ⋮ Standing waves on quantum graphs ⋮ Dirac operators on infinite quantum graphs ⋮ D^²=H+¼ with point interactions ⋮ NON-WEYL RESONANCE ASYMPTOTICS FOR QUANTUM GRAPH WITH THE DIRAC OPERATOR ON EDGES ⋮ Inverse problems for the Dirac operator on a star graph ⋮ Quantum spins on star graphs and the Kondo model ⋮ Partial inverse problems for Dirac operators on star graphs ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ On the nonlinear Dirac equation on noncompact metric graphs ⋮ Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮ Dirac-Krein systems on star graphs ⋮ A Borg–Levinson theorem for trees ⋮ Traces and inverse nodal problems for Dirac-type integro-differential operators on a graph ⋮ Weakly coupled states on branching graphs ⋮ An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity ⋮ A duality between Schroedinger operators on graphs and certain Jacobi matrices ⋮ Spectral properties of relativistic quantum waveguides ⋮ Zero modes of quantum graph Laplacians and an index theorem

Cites Work

• Quantum motion on two planes connected at one point
• Scattering problems on noncompact graphs
• Quantum motion on a half-line connected to a plane

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