A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs
arXiv:1902.00012 · doi:10.1007/978-3-030-60453-0
Abstract
In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss the specific features of the spectrum of the operator and, finally, we give some further details on the associated quadratic form (and on the form domain).
arXiv commentBook chapter in the volume "Mathematical Challenges of Zero-Range Physics: Models, Methods, Rigorous Results, Open Problems". 16 pages, 5 figures. Keywords: Dirac operator, metric graphs, spectral analysis, self-adjoint extensions, boundary triplets. arXiv admin note: text overlap with arXiv:1807.06937
References in corpus (16)
- The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
- Wave packets in Honeycomb Structures and Two-Dimensional Dirac Equations
- Spectral Statistics for the Dirac Operator on Graphs
- On the spectral theory of Gesztesy-Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
- NLS ground states on metric graphs with localized nonlinearities
- Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
- Bound states of the NLS equation on metric graphs with localized nonlinearities
- On the lack of bound states for certain NLS equations on metric graphs
- Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
- Dynamics of Dirac solitons in networks
- On the nonlinear Dirac equation on noncompact metric graphs
- Ground states of the -critical NLS equation with localized nonlinearity on a tadpole graph
- Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity
- Equilateral quantum graphs and boundary triples
- Dirac-Krein systems on star graphs
- Multiple solutions for a self-consistent Dirac equation in two dimensions
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