Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential

2012/07/31 by Zafar Ahmed
Mathematics · Physics and Astronomy · #Hermitian matrix #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Reciprocity (cultural anthropology) #Scattering #Unitarity #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/j.physleta.2013.02.031

published as Z.Ahmed, Phys. Lett. A 377 (2013) 957 · 7 pages. no figures and no tables, two corrections, appeared in Phys. Lett. A

openalex publication_date 2013/02/20 · arxiv created 2013/03/01 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in scattering from a complex PT-symmetric potential. In special cases, we show that this potential can even become invisible (R=0, T=1) from both left and right sides. We also find that this potential in a parametric regime enjoys a pseudo-unitarity of the type T+√R_leftR_right=1.

Citations

• Classical trajectories of the continuum states of the \chem\calPT symmetric Scarf II potential
• Must a Hamiltonian be Hermitian?
• Spectral singularities and Bragg scattering in complex crystals
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry