Observing complementary Lucas sequences using non-Hermitian zero modes

Quantum Physics [Submitted on 10 Apr 2026] Observing complementary Lucas sequences using non-Hermitian zero modes Li Ge The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are less well-known. In this work, we show that a special case of such complementary Lucas sequences can be observed on the same physical platform. It consists of a gain-and-loss-modulated non-Hermitian reservoir bridging two mirror-symmetric systems, which manifests the Lucas sequences in linearly localized edge states and a constant-intensity mode, respectively. Comments: 6 pages, 4 figures Subjects: Quantum Physics (quant-ph); Optics (physics.optics) Cite as: arXiv:2604.08919 [quant-ph]   (or arXiv:2604.08919v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.08919 Focus to learn more Submission history From: Li Ge [view email] [v1] Fri, 10 Apr 2026 03:28:30 UTC (659 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: physics physics.optics References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)