H. Hernandez-Coronado, D. Krejcirik, P. Siegl

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.

http://arxiv.org/abs/1011.4281

Mathematical Physics (math-ph); Quantum Physics (quant-ph)