Dynamical Localization for Discrete and Continuous Random Schrödinger Operators

Abstract:

We show for a large class of random Schrödinger operators H _ο on and on that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real,

Here ψ is a function of sufficiently rapid decrease, and P _I (H _ο) is the spectral projector of H _ο corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of H _ο and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.