Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics

• URL: http://arxiv.org/abs/2603.00256v1
• Date: Fri, 27 Feb 2026 19:09:46 GMT
• Title: Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics
• Authors: Vibhav Narayan Singh, Mohammad Umar, Mohammad Hasan, Bhabani Prasad Mandal,
• Abstract summary: We analytically derive locus equations for spectral singularities (SSs) and their time-reversed counterparts, coherent perfect absorption (CPA)<n>We show that reducing the Lévy index $$, which enhances nonlocal transport associated with Lévy-flight dynamics, systematically lowers the gain-loss strength required for the emergence of SSs and CPAs.<n>This study may find applications in fractional waveguides and metamaterials governed by fractional wave equations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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