New scattering features in non-Hermitian space fractional quantum mechanics

Highlights: • Space fraction quantum mechanics (SFQM) has been investigated with complex delta and barrier potentials. • New scattering features due to these potentials are obtained in SFQM. • Spectral Singular (SS) points are blue/red shifted when Levy index is decreased. • The oscillations in scattering coefficients around SS have interesting behaviors in SFQM. • Deeper relations between the scattering properties in standard QM and those of in SFQM are observed. - 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 Schrödinger equation. In the present work we explore these scattering features in the domain of non-Hermitian space fractional quantum mechanics (SFQM) governed by fractional Schrödinger equation which is characterized by Levy index $\alpha$ ($1<\alpha \le 2$). 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 $V\left(x\right)=i\rho \delta (x-x_0)$, $\rho >0$, the SS energy, $E_{ss}$, is blue or red shifted with decreasing $\alpha$ depending on 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 are 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.