Asymptotic fractional uncertainty principle for the Helmholtz equation with periodic scattering data
Abstract
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 Schr\"odinger equation. To achieve this, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.