Static and dynamical, fractional uncertainty principles

Kumar, Sandeep; Ponce Vanegas, Felipe; Vega, Luis

doi:10.1090/tran/8655

Static and dynamical, fractional uncertainty principles
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by Sandeep Kumar, Felipe Ponce Vanegas and Luis Vega PDF

Trans. Amer. Math. Soc. 375 (2022), 5691-5725 Request permission

Abstract:

We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound for the concentration of mass. We also consider the evolution when the initial datum is the Dirac comb in $\mathbb {R}$. In this case we find fluctuations that concentrate at rational times and that resemble a realization of a Lévy process. Furthermore, the evolution exhibits multifractality.

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