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

Abstract

A family of discrete Schr & ouml;dinger equations with imaginary and maximally non-Hermitian multiparametric potentials V(x, A, B, & mldr;) is studied. In the domain of unitarity-compatible parameters D (known as the domain of spontaneously unbroken PT - symmetry) the reality of all of the bound-state energies E-n(A, B, & mldr;) survives up to the maximally non-Hermitian "exceptional-point" extreme with parameters A((EP)), B-(EP), & mldr;. The computer-assisted proof of existence and the symbolic-manipulation localization of such a spectral-degeneracy limit are sampled showing that their complexity grows quickly with the number of parameters. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).