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

2025/03/04 by Canto, Javier, Schiavone, Nico Michele, Vega, Luis
#26A33 (Secondary) #81U30 (Primary) 35J05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.02868

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 Schrödinger equation. To achieve this, we first establish an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.

Related

• Static and Dynamical, Fractional Uncertainty Principles
• Stability for the Helmholtz equation in deterministic and random periodic structures
• Extremizers and Stability for Fractional L^p Uncertainty Principles
• Dispersive estimates for time and space fractional Schrödinger equations
• Fractional White-Noise Limit and Paraxial Approximation for Waves in Random Media