Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint

Abstract

A family of discrete Schrödinger equations with imaginary potentials $V(x)$ is studied. Inside the domain $\mathcal{D}$ of unitarity-compatible values of $V(x)$, the reality of all of the bound-state energies survives up to the ``exceptional-point'' (EP) maximally non-Hermitian spectral-degeneracy boundaries $\partial \mathcal{D}$. The computer-assisted localization of the EP limits is performed showing that the complexity of the task grows quickly with the number $N$ of grid points $x$.

22 pages, 3 figures

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Three-Hilbert-Space Formulation of Quantum Mechanics
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Intrinsic exceptional point -- a challenge in quantum theory

Cited by in corpus (1)

• Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation