Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Singh, Vibhav Narayan Umar, Mohammad Hasan, Mohammad Mandal, Bhabani Prasad |
| author_facet | Singh, Vibhav Narayan Umar, Mohammad Hasan, Mohammad Mandal, Bhabani Prasad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics Singh, Vibhav Narayan Umar, Mohammad Hasan, Mohammad Mandal, Bhabani Prasad Quantum Physics 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. |
| title | Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.00256 |