Ananya Ghatak, Brijesh Kumar Mourya, Raka Dona Ray Mandal, Bhabani Prasad Mandal (BHU)
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)
Ananya Ghatak, Raka Dona Ray Mandal, Bhabani Prasad Mandal (BHU)
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes imaginary. For one PT-symmetric case we have entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from left (or right) at certain discrete energies. The penetrating states in the other PT-symmetric configuration are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. Presence of MSS and reflectionlessness are also discussed for the free states in the later case.
http://arxiv.org/abs/1310.7752
Quantum Physics (quant-ph)