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 non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system.

http://arxiv.org/abs/1403.0539

Quantum Physics (quant-ph)

We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle can have open orbits even with real energy if it is initially placed in certain region between the two wells on the same side of the imaginary axis. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. At the classical level unlike the analogous quantum situation we do not see any qualitative differences in the features of the particle dynamics for PT symmetry broken and unbroken phases.

http://arxiv.org/abs/1312.0757
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)

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)

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)

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)

We consider non-Hermitian PT-symmetric deformation of \(A_{N-1}\) type Calogero model without confining potential to investigate the possible existence of spectral singularity. By considering the Wronskian between asymptotic incoming and outgoing scattering state wave functions, we found that there exist no spectral singularity in this model. We further explicitly show that the transmission coefficient vanishes and the reflection coefficient becomes unity for all values of the energy in such a momentum dependent non-Hermitian PT-symmetric model.

http://arxiv.org/abs/1209.0535
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

We bring out the existence of at most one spectral singularity (SS) and deep multiple minima in the reflectivity of the non-Hermitian (complex) Ginocchio potential. We find a parameter dependent single spectral singularity in this potential provided the imaginary part is emissive (not absorptive). The reflectionlessness of the real Hermitian Ginocchio’s potential at discrete positive energies gives way to deep multiple minima in reflectivity when this potential is perturbed and made non-Hermitian (complex). A novel co-existence of a SS with deep minima in reflectivity is also revealed wherein the first reflectivity zero of the Hermitian case changes to become a SS for the non-Hermitian case.

http://arxiv.org/abs/1207.1979

Quantum Physics (quant-ph)

We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.

http://arxiv.org/abs/1202.2413
Quantum Physics (quant-ph); Mathematical Physics (math-ph)