Quantum graphs: Self-adjoint, and yet exhibiting a nontrivial PT-symmetry
Abstract
We demonstrate that a quantum graph exhibits a 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.
- 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;
- PT-symmetry;
- Vertex coupling;
- Lattice transport properties;
- Mathematical Physics;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Mathematics - Spectral Theory;
- Quantum Physics;
- 81Q35;
- 35J10
- E-Print:
- 11 pages, four figures