Mathematical Physics
[Submitted on 10 Aug 2021
]
Title: Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{PT}$-symmetry
Title: 量子图：自伴的，但仍表现出非平凡的$\mathcal{PT}$-对称性
Abstract: We demonstrate that a quantum graph exhibits a $\mathcal{PT}$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not invariant with respect to transposition. We also illustrate how the transport properties of such graphs are significantly influenced by the presence or absence of the non-Robin component of the coupling.
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