Agenda
Mercredi 24 mars 2021
On the ensemble controllability of quantum systems via adiabatic methods
Nicolas Augier (INRIA Sophia-Antipolis)
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.
Random Schrödinger Operators arising in the study of aperiodic media
Constanza Rojas-Molina (CY Cergy Paris Université)
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)