Asymptotic Fractional Uncertainty Principle for the Helmholtz Equation with Periodic Scattering Data
Abstract
Abstract. We investigate the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. We show that, given appropriate rescaling, the interaction between different frequencies exhibits the same fluctuating behavior as that for the Schrödinger equation. Since the Helmholtz equation is the stationary form of various evolution equations, this suggests that such highly fluctuating behavior is a general feature of periodic scattering on the fractional scale and not specific to the Schrödinger setting. To achieve our result, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Mathematical Analysis and Transform Methods
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 868–887
- Publication date
- 4 March 2026
- Language
- EN