New scattering features in non-Hermitian space fractional quantum mechanics

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 $\alpha$ ($1<\alpha \le 2$). 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 $V(x)=-i\rho \delta (x-x_0)$, $\rho >0$, 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.

18 pages, 10 color figures

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Cited by in corpus (4)

• New scattering features of quaternionic point interaction in non-Hermitian quantum mechanics
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
• Emergence of Hermitian topology from non-Hermitian knots