• An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0063

• # Keywords

Non-Hermitian potential; coherent scattering; coherent perfect absorption; lasing; spectral singularity; real; complex conjugate; single non-real eigenvalue.

• # Abstract

The versatile and exactly solvable Scarf II potential has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector, it has gone underutilised. Here, we present the most simple analytic forms for the scattering coefficients $(T (k), R(k), | det S(k)|)$. On the one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand, they make new predictions – all simple and analytical. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of spectral singularity (SS) into a finite number of complex conjugate pairs of eigenvalues (CCPEs). NSDSS behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising coexistence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, so far, the complex Scarf II potential is not known to be pseudo-Hermitian ($η ^{−1}Hη = H^{†})$ under a metric of the type $η(x)$.

• # Author Affiliations

1. Theoretical Physics Section, Bhabha Atomic Research Centre, Mumbai 400 085, India
2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
3. Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India

• # Pramana – Journal of Physics

Volume 96, 2022
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Posted on July 25, 2019

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