Non-Lyapunov annealed decay for 1d Anderson eigenfunctions

Abstract

In Exact dynamical decay rate for the almost Mathieu operator by Jitomirskaya et al. [Math. Res. Lett. 27(3), 789–808 (2020)], the authors analysed the dynamical decay in expectation for the supercritical almost-Mathieu operator in function of the coupling parameter, showing that it is equal to the Lyapunov exponent of its transfer matrix cocycle, and asked whether the same is true for the 1d Anderson model. We show that this is never true for bounded potentials when the disorder parameter is sufficiently large.