Physics counterpart of the PT non-hermitian tight-binding chain

Details Physics counterpart of the PT non-hermitian tight-binding chain Physics counterpart of the PT non-hermitian tight-binding chain

2010-01-22

arxiv.org/abs/1001.3949v1

Phys.Rev.A81:032109,2010

Physics

Quantum Physics

6 pages, 3 figures

Scientific paper

10.1103/PhysRevA.81.032109

We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any real-energy eigenstate of a PT tight-binding lattice with on-site imaginary potentials shares the same wave function with a resonant transmission state of the corresponding Hermitian lattice embedded in a chain. It indicates that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the resonance transmission state of the extended Hermitian Hamiltonian.

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