Conditional observability versus self-duality in a schematic model

Abstract

In a simple PT-symmetric model we demonstrate that and how the violation of a reflection symmetry $E_j=-E_{N+1-j}$ of the spectrum (called "self-duality" by Dunne and Shifman) is connected with the loss of the simplicity of the shape of the boundary of the domain D of parameters where the Hamiltonian H is quasi-Hermitian, i.e., where all the bound-state energies are real.

11 pages, 2 figures

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• A return to observability near exceptional points in a schematic PT-symmetric model
• Conditional observability
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model