Dynamical Localization for the One-dimensional Continuum Anderson Model in a Decaying Random Potential

Abstract

We consider a one-dimensional continuum Anderson model where the potential decays in average like $|x{|}^{-\alpha }$, $\alpha >0$. We show dynamical localization for $0<\alpha <\frac{1}{2}$ and provide control on the decay of the eigenfunctions.