Les séminaires auront lieu à l'
Institut Henri Poincaré, habituellement en salle 314.
Le séminaire est financé par le GDR "Dynamique quantique" du CNRS.
Pour tout renseignement complémentaire, veuillez contacter les organisateurs, Hakim Boumaza, Mathieu Lewin ou Stéphane Nonnenmacher.
|11h15 - 12h15||Constanza Rojas-Molina (Bonn)
||Characterization of the metal-insulator transport transition for the two-particle Anderson model
In dimensions higher than two it is expected that a disordered system, modeled by an Anderson operator, undergoes a metal-insulator transition from a region of localization to delocalization. For the one-particle Anderson model, F. Germinet and A. Klein showed that the transport exponent in these regions can be related to the applicability of the multiscale analysis method used in the proof of localization. In this talk we will present a recent generalization of this characterization to the two-particle Anderson model with short-range interactions. We show that, for any fixed number of particles, the slow spreading of wave packets in time implies the initial estimate of a modified version of the Bootstrap Multiscale Analysis. In the case of two particles, this gives a characterization of the metal-insulator transport transition.
This is joint work with A. Klein and Son T. Nguyen.
|14h - 15h||Alberto Maspero (Nantes)
||On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms
We study well-posedness and growth of Sobolev norms for
time dependent Schrödinger equations of the form
i∂tψ =(H+V(t))ψ, where H is a self-adjoint positive operator, while V(t) is a perturbation smoothly depending on time.
Under the assumptions that the spectrum of H can be enclosed in spectral clusters whose distance is increasing and
V(t) is a relatively bounded perturbation of H, we prove that the Sobolev norms of the solution grow at most as tε when t increases, for any ε>0. If V(t) is analytic in time we improve the bound to (log t)γ, for some γ>0.
The proof follows the strategy, due to Joye and Nenciu, of the adiabatic approximation of the flow. We apply our result to Schrödinger operators on R and Schrödinger operators on Zoll manifolds.
This is a joint work with Didier Robert.
|15h15 - 16h15|| Isabelle Tristani (X)
|| On the inhomogeneous Landau equation.
This work deals with the inhomogeneous Landau equation on the torus (only in the cases for which we have the existence of a spectral gap for the linearized problem). We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct perturbative solutions (close to the equilibrium). Finally, we prove the exponential stability of these solutions.
This is a joint work with K. Carrapatoso and K.-C. Wu.