We observe that the reflection and transmission coefficients of a particle within a double, PT-symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no spontaneous breakdown of PT symmetry. The potential profile in the intermediate layer is considered such that it has a non vanishing imaginary part near the heterojunctions. Exact analytical solutions for the wave function are obtained, and the reflection and transmission coefficients are plotted as a function of energy, for both left as well as right incidence. As expected, the spatial dependence on mass changes the nature of the scattering solutions within the heterojunctions, and the space-time (PT) symmetry is responsible for the left-right asymmetry in the reflection and transmission coefficients. However, the non vanishing imaginary component of the potential near the heterojunctions gives new and interesting results.

http://arxiv.org/abs/1306.2226

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

We apply the factorization technique developed by Kuru et. al. [Ann. Phys. {\bf 323} (2008) 413] to obtain the exact analytical classical trajectories and momenta of the continuum states of the non Hermitian but \(\cal{PT}\) symmetric Scarf II potential. In particular, we observe that the strange behaviour of the quantum version at the spectral singularity has an interesting classical analogue.

http://arxiv.org/abs/1206.6987
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain — when the region within the heterojunctions is described by a non Hermitian \({\cal{PT}}\) symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian \({\cal{PT}}\) symmetric systems — viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.

http://arxiv.org/abs/1204.2416

Quantum Physics (quant-ph)