{"user_id":"69187","abstract":[{"text":"Exceptional points (EPs) occurring in non-Hermitian systems at certain\nphysical parameters are intensively studied in many areas of physics, including\ndiffraction optics, lasers, atomic and polaritonic condensates, often in the\ncontext of sensing. Recent discoveries of EPs in nonlinear systems open the\ndoor for an even larger parameter space, raising the question of whether the\ngeometric structure of EPs is universal and independent of the physical model.\nWe show that this is the case for nonlinear perturbations of an isolated\n2nd-order linear EP which becomes the organizing point of a universal\nelementary catastrophe (elliptic umbilic). This clarifies not only the\nneighborhood's topology but also its geometric shape (cone with quasi-deltoid\ncross section). Thus, the position and characteristics of EPs can be predicted\nin nonlinear non-Hermitian parameter space; e.g., at a 2nd-order linear EP four\nnonlinear eigenvectors coalesce. These fundamental insights on universal\ntopological structures and phase boundaries accompanying EPs in nonlinear\nphysical systems will pave the way for the purposeful design of such systems\nwith novel functionalities and control possibilities.","lang":"eng"}],"status":"public","citation":{"ieee":"N. H. Kwong <i>et al.</i>, “Universal neighborhood topology and geometry of exceptional points in   physical systems,” <i>arXiv:2502.19236</i>. 2025.","ama":"Kwong NH, Wingenbach J, Ares L, et al. Universal neighborhood topology and geometry of exceptional points in   physical systems. <i>arXiv:250219236</i>. Published online 2025.","mla":"Kwong, N. H., et al. “Universal Neighborhood Topology and Geometry of Exceptional Points in   Physical Systems.” <i>ArXiv:2502.19236</i>, 2025.","chicago":"Kwong, N. H., Jan Wingenbach, Laura Ares, Jan Sperling, Xuekai Ma, Stefan Schumacher, and R. Binder. “Universal Neighborhood Topology and Geometry of Exceptional Points in   Physical Systems.” <i>ArXiv:2502.19236</i>, 2025.","apa":"Kwong, N. H., Wingenbach, J., Ares, L., Sperling, J., Ma, X., Schumacher, S., &#38; Binder, R. (2025). Universal neighborhood topology and geometry of exceptional points in   physical systems. In <i>arXiv:2502.19236</i>.","short":"N.H. Kwong, J. Wingenbach, L. Ares, J. Sperling, X. Ma, S. Schumacher, R. Binder, ArXiv:2502.19236 (2025).","bibtex":"@article{Kwong_Wingenbach_Ares_Sperling_Ma_Schumacher_Binder_2025, title={Universal neighborhood topology and geometry of exceptional points in   physical systems}, journal={arXiv:2502.19236}, author={Kwong, N. H. and Wingenbach, Jan and Ares, Laura and Sperling, Jan and Ma, Xuekai and Schumacher, Stefan and Binder, R.}, year={2025} }"},"date_created":"2025-03-07T10:17:39Z","author":[{"full_name":"Kwong, N. H.","first_name":"N. H.","last_name":"Kwong"},{"first_name":"Jan","last_name":"Wingenbach","full_name":"Wingenbach, Jan"},{"full_name":"Ares, Laura","last_name":"Ares","first_name":"Laura"},{"first_name":"Jan","last_name":"Sperling","full_name":"Sperling, Jan"},{"full_name":"Ma, Xuekai","first_name":"Xuekai","last_name":"Ma"},{"last_name":"Schumacher","first_name":"Stefan","full_name":"Schumacher, Stefan"},{"last_name":"Binder","first_name":"R.","full_name":"Binder, R."}],"title":"Universal neighborhood topology and geometry of exceptional points in\n  physical systems","type":"preprint","date_updated":"2025-03-07T10:19:44Z","_id":"58932","publication":"arXiv:2502.19236","external_id":{"arxiv":["2502.19236"]},"year":"2025"}