Abstract
Non-Hermitian quantum one-parametric N by N matrix Hamiltonians H^(N)(λ) with real spectra are considered. Their special choice H^(N)(λ)=J^(N)+λV^(N)(λ) is studied at small λ, with a general N²-parametric real-matrix perturbation λV^(N)(λ), and with the exceptional-point-related "unperturbed" Jordan-block Hamiltonian J^(N). A "stability corridor" S of the parameters λ is then sought guaranteeing the reality of spectrum and realizing a unitary-system-evolution access to the exceptional-point boundary of stability. The corridors are then shown N-dependent and "narrow", corresponding to certain specific, unitarity-compatible perturbations with "admissible" matrix elements V^(N)_j+k,j(λ) = O(λ^(k-1)/2) at subscripts k=1,2,…,N-1 and at all j.