Origin of branch points in the spectrum of PT-symmetric periodic potentials
arXiv:0908.3354 · doi:10.1103/PhysRevA.80.042105
Abstract
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.
6 pages, 5figures
References in corpus (10)
- Making Sense of Non-Hermitian Hamiltonians
- Visualization of Branch Points in PT-Symmetric Waveguides
- Faster than Hermitian Quantum Mechanics
- An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
- Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
- Scattering in PT-symmetric quantum mechanics
- Conceptual Problems in Scattering from Localized non-Hermitian Potentials
- Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
- Scattering theory with localized non-Hermiticities
- Spiked potentials and quantum toboggans