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

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

2009-08-24

arxiv.org/abs/0908.3354v1

Physics

Quantum Physics

6 pages, 5figures

Scientific paper

There exists multiple branch points in the energy spectrum for some \emph{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.

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