Perfect transmission scattering as a PT-symmetric spectral problem

Details Perfect transmission scattering as a PT-symmetric spectral problem Perfect transmission scattering as a PT-symmetric spectral problem

2010-11-18

arxiv.org/abs/1011.4281v1

Phys. Lett. A 375 (2011), 2149-2152

Physics

Mathematical Physics

7 pages, 5 figures

Scientific paper

We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the other hand, the scattering data can serve to describe the spectrum of a large class of Schroedinger operators with complex Robin boundary conditions.

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