Stanislav A. Stepin

Phase integrals method in the problem of quasiclassical localization of spectrum

An approach based on phase integrals method will be outlined that enables one to examine quasiclassical asymptotics of spectrum for nonselfadjoint singularly perturbed operators. This approach is applied then to boundary eigenvalue problem for second order differential operators with PT-symmetric cubic potentials of generic type. Bohr-Sommerfeld quantization rules are derived to describe the location of the spectrum and geometric properties of the corresponding spectrum concentration curves are investigated as well.