2025/09/01 by Yidan Wang, Wang, Yidan, Xuesen Na +7
Mathematics · Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Optics (physics.optics) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2509.01782
openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's density of states. We investigate one-dimensional scattering with general dispersion relations of the form ε(k) = |k|m and ε(k) = sign(k)|k|m for any real m ≥ 1. For key models such as emitter scattering and separable potentials, we prove that the low-energy S-matrix converges to universal forms determined solely by the dispersion exponent m and a few integers defining the interaction. This establishes a broad classification of new universality classes, extending far beyond the standard quadratic dispersion paradigm. Furthermore, we derive a generalized Levinson's theorem relating the total winding of the scattering phase to the number of bound states. Our findings are directly relevant to synthetic quantum systems, where engineered dispersion relations in atomic arrays and photonic crystals offer a platform to explore these universal behaviors.