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

Abstract

We demonstrate that a quantum graph exhibits a $\mathcal{P}\mathcal{T}$-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.

arXiv comment11 pages, four figures

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Cited by in corpus (4)

• Kagome network with vertex coupling of a preferred orientation
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Magnetic ring chains with vertex coupling of a preferred orientation
• Magnetic square lattice with vertex coupling of a preferred orientation