A family of quantum graph vertex couplings interpolating between different symmetries

Abstract

The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the interpolation family in terms of circulant matrices, we analyze the spectral and scattering property of such vertices, and investigate the band spectrum of the corresponding square lattice graph.

arXiv commentrevised version; 24 pages, 5 figures

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Cited by in corpus (2)

• Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{P}\mathcal{T}$-symmetry
• Topologically induced spectral behavior: the example of quantum graphs