L\'{e}vy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics
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Quantum Physics arXiv:2603.00256 (quant-ph) [Submitted on 27 Feb 2026] 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 View a PDF of the paper titled L\'{e}vy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics, by Vibhav Narayan Singh and 3 other authors View PDF HTML (experimental) 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 $\alpha$, 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 $\alpha$ induces a blue shift of the SS energy, in direct agreement with earlier studies. From this perspective, the Lévy index $\alpha$ 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. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.00256 [quant-ph] (or arXiv:2603.00256v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.00256 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vibhav Narayan Singh [view email] [v1] Fri, 27 Feb 2026 19:09:46 UTC (510 KB) Full-text links: Access Paper: View a PDF of the paper titled L\'{e}vy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics, by Vibhav Narayan Singh and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)