Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a PT symmetric (hence parity violating) complex potential which admits penetrating state solutions analytically for all possible values of incidence energy and (ii) reciprocity is shown to hold at certain discrete energies for two other parity violating complex potentials.

http://arxiv.org/abs/1410.7886
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)

We consider a 2d anisotropic SHO with \(\bf ixy\) interaction and a 3d SHO in an imaginary magnetic field with \(\vec\mu_l\). \(\vec B\) interaction to study the PT phase transition analytically in higher dimension.Unbroken PT symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system. PT phase transition ceases to occur the moment the 2d oscillator becomes isotropic.Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes PT phase transition depending on the strength of the magnetic field and frequency of the oscillator.

http://arxiv.org/abs/1301.2387
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)