The mathematical link between murmurations and classical physics
Nina Zubrilina proved an explicit formula showing that murmuration averages asymptotically follow functions related to Airy functions.
Airy functions appear in quantum mechanics (quantum tunneling), optics (diffraction), and fluid dynamics. Their appearance in number theory was unexpected.
This suggests deep connections between arithmetic and physics.
Both Airy functions and murmurations show characteristic oscillations that decay as the argument increases. The frequency increases while amplitude decreases.
This self-similar behavior is the signature of Airy asymptotics.