Static and Dynamical, Fractional Uncertainty Principles

Sandeep Kumar; Felipe Ponce-Vanegas; Luis Vega

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arXiv · 2103.03794

Static and Dynamical, Fractional Uncertainty Principles

Sandeep Kumar·Felipe Ponce-Vanegas·Luis Vega

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Abstract

We study the process of dispersion of low-regularity solutions to the Schr\"odinger 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 consider also 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 L\'evy process. Furthermore, the evolution exhibits multifractality.

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Sandeep Kumar, Felipe Ponce-Vanegas, Luis Vega. 2021-03-05. Static and Dynamical, Fractional Uncertainty Principles. https://arxiv.org/abs/2103.03794

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