We investigate the scattering features of a non-Hermitian rectangular potential within the framework of space-fractional quantum mechanics. Using the Riesz fractional derivative, we analytically derive locus equations for spectral singularities (SSs) and their time-reversed counterparts, coherent perfect absorption (CPA), in a dimensionless complex-potential parameter space. This geometric locus formulation provides a transparent representation of the SS and CPA conditions and enables direct visualization of how fractional quantum dynamics modifies non-Hermitian scattering. We show that reducing the Lévy index
α, which enhances nonlocal transport associated with Lévy-flight dynamics, systematically lowers the gain-loss strength required for the emergence of SSs and CPAs, while increasing the mode index further suppresses this threshold. In addition, for fixed potential parameters, we demonstrate that decreasing
α induces a blue shift of the SS energy, in direct agreement with earlier studies. From this perspective, the Lévy index
α emerges as a tunable control knob for SS-CPA settings in fractional non-Hermitian quantum systems. Beyond its quantum-mechanical setting, this study may find applications in fractional waveguides and metamaterials governed by fractional wave equations. This work also bridges the gap between non-Hermitian quantum mechanics and space-fractional quantum mechanics.
Spectral singularities have been extensively studied over the last one and half decades for different non-Hermitian potentials in non-Hermitian quantum mechanics. The nature of spectral singularities has not been studied for the case of quaternionic potential. In the present work, we perform an analytical study on scattering from a quaternionic point interaction represented by a delta function. New features of spectral singularities are observed, which are different than the case of a complex (non-quaternionic) point interaction. The most notable difference is the occurrence of spectral singularity from the lossy point interaction, which is forbidden in the case of standard non-Hermitian quantum mechanics.
We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential Vr − iVi in space-fractional quantum mechanics. By applying the stationary phase method, we derive a closed-form expression for the tunneling time for this system. This study presents the first investigation of tunneling time at the interplay of non-Hermitian quantum mechanics and space-fractional quantum mechanics. The variation in tunneling time as the system transitions from a real to a complex potential is analyzed. We demonstrate that the tunneling time exhibits a dependence on the barrier width d in the limit d → ∞, showing the absence of the Hartman effect. A particularly striking feature of our findings is the potential manifestation of the Hartman effect for a specific combination of the absorption component Vi and the Levy index α. This behavior arises from the fact that the presence of the absorption component Vi leads to a monotonic increase in tunneling time with barrier thickness, whereas the Levy index α reduces the tunneling time. The interplay of these contrasting influences facilitates the emergence of the Hartman effect under a specific combination of Vi and the fractional parameter α.