Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{PT}$-symmetry

• URL: http://arxiv.org/abs/2108.04708v1
• Date: Tue, 10 Aug 2021 14:11:55 GMT
• Title: Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{PT}$-symmetry
• Authors: Pavel Exner, Milos Tater
• Abstract summary: We demonstrate that a quantum graph exhibits a $mathcalPT$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices. 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.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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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