Quantum star-graph analogues of PT-symmetric square wells. II: Spectra

Abstract

For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric complex Robin boundary conditions, the spectrum is obtainable in a closed asymptotic-expansion form, in principle at least. Explicit formulae up to the second order are derived for illustration, and a few comments on their consequences are added.

12 pages, 1 figure, a complement of part I (arXiv 1205.5211)

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• Scattering in the PT-symmetric Coulomb potential
• Quantum star-graph analogues of PT-symmetric square wells

Cited by in corpus (2)

• Quantum Graphs: $\mathcal{P}\mathcal{T}$-symmetry and reflection symmetry of the spectrum
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase