APDE seminar@BCAM: Fractional dispersion properties of solutions to the Helmholtz equation with periodic scattering data

In this talk, we explore some properties of solutions to the Helmholtz equation. More precisely, we show that under mild regularity conditions, an asymptotic fractional uncertainty principle holds. We apply this result to a particular solution with periodic scattering data, and we obtain a very intriguing object with fluctuating behaviour that has been previously observed in solutions to the Schrödinger equation. We claim that this is tied to the Talbot effect.  

This talk is based on joint work with N. M. Schiavone (UPM) and L. Vega (EHU & BCAM)