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arXiv · 1712.09727

New scattering features in non-Hermitian space fractional quantum mechanics

Mohammad Hasan·Bhabani Prasad Mandal
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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 $α$ ($ 1< α\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 $V(x)=-iρδ(x-x_{0})$, $ρ> 0$, the SS energy, $E_{ss}$, is blue or red shifted with decreasing $α$ 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.

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Mohammad Hasan, Bhabani Prasad Mandal. 2017-12-23. New scattering features in non-Hermitian space fractional quantum mechanics. https://doi.org/10.1016/j.aop.2018.07.008

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