Various scattering properties of a new PT-symmetric non-Hermitian potential

Abstract

We complexify a 1-d potential V (x) = V 0 cosh 2 µ{tanh[(x − µd)/d] + tanh(µ)} 2 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 (µ, d) becomes imaginary. For the case of µ → iµ, 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 case (d → id) 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.

Hartman effect from layered PT-symmetric system

“…The non-Hermitian Hamiltonian display several new features which are originally absent in Hermitian Hamiltonians. The important features are exceptional points (EPs) [30,31], spectral singularity (SS) [32,33],coherent perfect absorption (CPA) [34]- [38], critical coupling (CC) [39]- [42] and CPA-laser [43]. Others notable features are invisibility [44,45,46] and reciprocity [47].…”

Scattering amplitudes for the rationally extended PT symmetric complex potentials

“…Since the last one and half decades, the P T symmetric non-hermitian systems have been developed considerably and have found several applications in optics as well as other branches of physics [14,15,16,17,18,19,20,21]. Some of the important properties such as the existence of spectral singularity (divergence of both reflection and transmission co-efficients at a point) [22,23,24,25,26], exceptional points (coalesce of two energy levels along with their eigenfunctions at certain points in the complex plane) [27,28,29,30], Handedness effect (dependence of reflection coefficient on the direction of wave) [31] have been also observed in such systems.…”

A black potential for spin less particles

“…Non-Hermitian theories have very rich scattering properties. Various features of scattering due to non-Hermitian potential like exceptional points (EPs) [13]- [15], spectral singularity (SS) [16]- [19], invisibility [18]- [21], reciprocity [18]- [22], coherent perfect absorption (CPA) [23]- [31] and critical coupling (CC) [32]- [36] have generated huge interests during last few years due to their applicability and usefulness in the study of different optical systems. CPA or CC, the time reversal of lasing effect has become very exciting due to the discovery of anti-laser [23]- [25] which has number of applications in optical computer, radiology etc.…”