Non-Weyl resonance asymptotics for quantum graph with the Dirac operator on edges. (English) Zbl 1537.81102
Summary: We investigate quantum graph consisting of a compact interior with a finite number of semi-infinite edges attached. The Dirac operator acts on the edges of the graph. At vertices, matching conditions of a general form are considered. For this model, the non-Weyl asymptotics of resonances (quasi-eigenvalues) is studied. The results were obtained by constructing an effective coupling matrix.
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 35B34 | Resonance in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 03D45 | Theory of numerations, effectively presented structures |
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