## One Citation

Ring chains with vertex coupling of a preferred orientation

- MathematicsReviews in Mathematical Physics
- 2020

We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length [Formula: see text] with the vertex…

## References

SHOWING 1-10 OF 37 REFERENCES

PT-symmetric quantum graphs

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

We consider PT-symmetric quantum graphs, in which the branching points provide PT-symmetric boundary conditions for the Schrödinger equation on a graph. For such branched quantum wires, we derive…

RT-symmetric Laplace operators on star graphs : real spectrum and self-adjointness

- Physics, Mathematics
- 2015

How ideas of -symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown…

A family of quantum graph vertex couplings interpolating between different symmetries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the δ type and a coupling introduced recently by two of the authors which exhibits a preferred…

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

- Mathematics
- 1998

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new…

Quantum graphs: PT -symmetry and reflection symmetry of the spectrum

- Mathematics
- 2017

Not necessarily self-adjoint quantum graphs—differential operators on metric graphs—are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P . If the…

Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

- Physics, Mathematics
- 1998

Abstract We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix…

Non-self-adjoint graphs

- Mathematics
- 2014

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a…

The self-adjointness of Hermitian Hamiltonians

- Mathematics
- 1993

For several examples of Hermitian operators, the issues involved in their possible self-adjoint extension are shown to conform with recognizable properties in the solutions to the associated…