The principal issue that will be developed in this talk is how to control

a parameter-dependent family of quantum systems with a common control input,

that is, the ensemble controllability problem. Thanks to the study one-parametric

families of Hamiltonians and their generic singularities when the system is driven

by two real inputs, we will give an explicit adiabatic control strategy for the

ensemble controllability problem when geometric conditions on the spectrum of

the Hamiltonian are satisfied, in particular, the existence of conical or

semi-conical intersections of eigenvalues.
Then, in order to understand which controllability properties can be extended

to the case where the system is driven by a single real input, we will study the

compatibility of the adiabatic approximation with the rotating wave approximation.

In this talk we review some recent results on random Schrödinger operators,
a standard framework for the study of the absence of wave propagation in random media, a phenomenon known
as Anderson localization. We focus on the case where the random medium is given by a random potential with
aperiodic underlying structure, which breaks the ergodicity of the model. We will see how information on the localization properties
for these non-ergodic models can be applied to
study the spectral and dynamical properties of Delone operators. The latter are deterministic models associated to
aperiodic structures (quasi-crystals). This is joint work with Peter Müller (LMU München)