Asymptotic fractional uncertainty principle for the Helmholtz equation with periodic scattering data

We investigate the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. We show that, under appropriate rescaling, the interaction between the different frequencies exhibits the same fluctuating behavior as for the Schrödinger equation. To achieve this, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.