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Bound states, scattering states and resonant states in PT-symmetric open quantum systems


We study the point spectrum and transmission scattering spectrum in extended optical lattice models incorporating balanced elements of energy amplification and attenuation in a central scattering region.  These serve as prototype models to illustrate more general concepts relevant to PT-symmetric physics in an open systems context.  For a given system geometry, we study two boundary conditions: purely outgoing waves and scattering states.  For the boundary condition consisting of purely outgoing waves we obtain the discrete spectrum associated with the scattering region.  In this case we reveal that, unlike the Hermitian case, PT-symmetric open quantum systems permit eigenstates with complex-valued eigenvalues to appear in the first Riemann sheet in the complex energy plane.  We also demonstrate the presence of and classify two different types of exceptional points appearing in the discrete eigenvalue spectrum.  We also demonstrate the presence of what we term a resonance in continuum (RIC) for certain parameter values.  Finally, we consider the scattering wave boundary conditions, under which we demonstrate that further imposing PT-symmetry on our scattering state results in a perfect transition through the scattering region.