Application of Lie transform perturbation method for multidimensional non-Hermitian systems

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.