Maximal couplings in PT-symmetric chain-models with the real spectrum of energies

Abstract

The domain $\mathcal{D}$ of all the coupling strengths compatible with the reality of the energies is studied for a family of non-Hermitian $N$ by $N$ matrix Hamiltonians $H^{(N)}$ with tridiagonal and $\mathcal{P}\mathcal{T}-$symmetric structure. At all dimensions $N$, the coordinates are found of the extremal points at which the boundary hypersurface $\partial \mathcal{D}$ touches the circumscribed sphere (for odd $N=2M+1$) or ellipsoid (for even $N=2K$).

18 pp., 2 figs

References in corpus (3)

• A return to observability near exceptional points in a schematic PT-symmetric model
• A Positive-Definite Scalar Product for Free Proca Particle
• Third order spectral branch points in Krein space related setups: PT-symmetric matrix toy model, MHD alpha^2-dynamo, and extended Squire equation

Cited by in corpus (8)

• Scattering theory with localized non-Hermiticities
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Discrete PT-symmetric models of scattering
• Conditional observability
• Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
• Classification of the conditionally observable spectra exhibiting central symmetry
• On the Spectrum of a Discrete Non-Hermitian Quantum System
• Conditional observability versus self-duality in a schematic model