| Abstract: |
| We discuss the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. Under suitable rescaling, the interaction between different frequencies exhibits the same fluctuating behavior found in the Schr\{o}dinger equation. Since the Helmholtz equation represents the stationary form of various evolution equations, these phenomena appear to be a general feature of periodic scattering at the fractional scale. Our results are based on establishing an asymptotic fractional uncertainty principle for solutions to the Helmholtz equation.
Joint work with Javier Canto (UPV/EHU) and Luis Vega (UPV/EHU, BCAM). |
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