Ananya Ghatak, Bhabani Prasad Mandal

To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating pos- itive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

http://arxiv.org/abs/1305.2022

Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)

Mohammad-Ali Miri, Matthias Heinrich, Demetrios N. Christodoulides

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.

http://arxiv.org/abs/1305.1689

Optics (physics.optics); Mathematical Physics (math-ph); Quantum Physics (quant-ph)