Semiclassical quantization of non-Hermitian 2-D systems: Classical (Lie transform) Perturbation theory

Both real and complex semiclassical eigen energies of two dimensional non-Hermitian Hamiltonian systems are obtained by classical (Lie transform) perturbation theory requiring the action variables I1 and I2 to satisfy the quantization condition I1=(n1+(1/2))ℏ and I2=(n2+(1/2))ℏ respectively where n1, n2 are integers. Classical perturbation theory with Lie transform makes classical trajectories, which are non-periodic or non-quasi-periodic, periodic. It was observed that this method produces accurate eigen energies even when classical trajectories are not periodic or quasi-periodic. Eigen energies obtained by classical perturbation theory are compared with the same, determined by Rayleigh-Schroedinger perturbation theory.

Keywords: Lie transform, non-Hermitian systems, semiclassical quantization

doi :10.4038/jnsfsr.v37i2.1066

J.Natn.Sci.Foundation Sri Lanka 2009 37 (2):111-115