Static and Dynamical, Fractional Uncertainty Principles

2021/03/05 by Kumar, Sandeep, Ponce-Vanegas, Felipe, Vega, Luis
#35B99 #35J10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.03794

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 consider also the evolution when the initial datum is the Dirac comb in 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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