Wave Transport and Localization in Prime Number Landscapes

In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest intrinsic complexity prime number distributions in imaginary quadratic fields. particular, address structure-property relationships scattering through elements nine fields (i.e., their associated rings integers) with class one, which are unique factorization domains (UFDs). Our theoretical analysis combines rigorous Green’s matrix solution multiple problem interdisciplinary methods spatial statistics graph theory point patterns to unveil relevant structural produce effects. The onset a Delocalization-Localization Transition (DLT) is demonstrated by comprehensive spectral Thouless as function optical density. Furthermore, employ Multifractal Detrended Fluctuation Analysis (MDFA) establish multifractal scaling local density states these complex discover direct connection between localization, multifractality, connectivity properties. Finally, use semi-classical approach demonstrate characterize strong coupling regime quantum emitters embedded environments. provides access engineering design rules for fabrication more efficient classical sources well photonic devices enhanced light-matter interaction based on numbers algebraic