Origin of branch points in the spectrum of PT-symmetric periodic potentials

الأصل · EN

There exists multiple branch points in the energy spectrum for some PT-symmetric periodic potentials, where the real eigenvalues turn into complex ones. By studying the transmission amplitude for a localized complex potential, we elucidate the physical origin of the breakdown of perturbation method and Born approximation. Mostly importantly, we derive an analytic criteria to determine why, when and where the bifurcation will occur.