Perfect transmission scattering as a PT-symmetric spectral problem

TL;DR

This paper links perfect transmission scattering to PT-symmetric operators, offering a physical framework for quasi-Hermitian quantum mechanics and analyzing how complex eigenvalues affect transmission properties.

Contribution

It introduces a PT-symmetric spectral problem framework for perfect transmission scattering and explores the impact of complex eigenvalues on transmission energies.

Findings

Complex eigenvalues cause loss of perfect transmission energies.

Scattering data describes spectra of Schrödinger operators with complex boundary conditions.

PT-symmetry provides a physical basis for quasi-Hermitian quantum mechanics.

Abstract

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.