Quantum graphs: Selfadjoint, and yet exhibiting a nontrivial PTsymmetry
Abstract
We demonstrate that a quantum graph exhibits a PTsymmetry 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 nonRobin component of the coupling.
 Publication:

Physics Letters A
 Pub Date:
 November 2021
 DOI:
 10.1016/j.physleta.2021.127669
 arXiv:
 arXiv:2108.04708
 Bibcode:
 2021PhLA..41627669E
 Keywords:

 Quantum graph;
 PTsymmetry;
 Vertex coupling;
 Lattice transport properties;
 Mathematical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematics  Spectral Theory;
 Quantum Physics;
 81Q35;
 35J10
 EPrint:
 11 pages, four figures