Multiscale reference function analysis of the \(\mathcal{PT}\) symmetry breaking solutions for the \(P^2+iX^3+i\alpha X\) Hamiltonian (Q2757876)

From the conclusion: We have confirmed the asymptotic analysis prediction of Delabaerre and Trinh (DT) on the existence of symmetry breaking solutions for the \(H_\alpha\) Hamiltonian. Our methods enable the precise analysis of the complex-real spectra, particularly for moderate \(\alpha\) values at the limits of their DT asymptotic validity. The results of both an eigenenergy estimation method (MRF) and an eigenenergy bounding method were presented. The algebraic simplicity and ease of computational implementability of the MRF method recommends it highly for application to similar problems. Through the use of readily available algebraic programming software, the MRF approach can be extended to arbitrary precision.