New scattering features in non-Hermitian space fractional quantum mechanics

TL;DR

This paper investigates new scattering phenomena in non-Hermitian space fractional quantum mechanics, revealing enhanced flexibility and novel features of spectral singularities and coherent perfect absorption compared to standard quantum mechanics.

Contribution

It extends the study of SS and CPA to non-Hermitian space fractional quantum mechanics, uncovering new scattering features and the influence of Levy index on these phenomena.

Findings

SS energy shifts with Levy index in delta potential

Oscillatory reflection and transmission near SS in fractional systems

Development of SS and CPA features in fractional quantum barriers

Abstract

The spectral singularity (SS) and coherent perfect absorption (CPA) have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian standard quantum mechanics (SQM) governed by Schrodinger equation. In the present work we explore these scattering features in the domain of non-Hermitian space fractional quantum mechanics (SFQM) governed by fractional Schrodinger equation which is characterized by Levy index $\alpha$ ($ 1< \alpha \leq 2$). We observe that non-Hermitian SFQM systems have more flexibility for SS and CPA and display some new features of scattering. For the delta potential $V(x)=-i\rho \delta (x-x_{0})$, $\rho > 0$, the SS energy, $E_{ss}$, is blue or red shifted with decreasing $\alpha$ depending the strength of the potential. For complex rectangular barrier in non-Hermitian SQM, it is known that the reflection and transmission amplitudes are oscillatory near the spectral singular point. It is found that these oscillations eventually develop SS in non-Hermitian SFQM. The similar features is also reported for the case of CPA phenomena from complex rectangular barrier in non-Hermitian SFQM. These observations suggest a deeper relation between scattering features of non-Hermitian SQM and non-Hermitian SFQM.